The Trump administration probably cannot negotiate a comprehensive deal for Ukraine immediately and will need to come up with an initial solution to try and halt the fighting. Doing so is a rocky road ahead, partly because the Russians have zero trust in anything coming from the west, partly because the Ukrainians are unwilling partners, and partly because Europe wants to continue the war.

President Trump in an interview with the New York Post says that he has had at least one telephone call with Russian President Vladimir Putin, maybe more. The Kremlin has not confirmed, nor have they denied, that calls have taken place, but officially Russia says it has not received any proposals from the US side.
Meanwhile, the US is sending Vice President J.D. Vance and retired General Keith Kellogg to the Munich Security Conference. Zelensky will also attend the meeting, Kellogg says that he is preparing "options" for President Trump but won't reveal them at the Munich conference.

It is not clear what can be accomplished in Munich. In fact, US high level participation at the Munich conference could actually set back any deal with Russia, as America's European colleagues are pushing for more war, not less. (Of course, the Europeans expect America to keep footing the bill for the conflict.)
Russia sees little or no reason to bargain with Zelensky or with the Europeans. Putin, however, clearly favors negotiating with the United States. Apparently Putin thinks the only possible deal will be between Russia and the US, if a deal can be found.
On the battlefield the Ukrainians have thrown in additional reserves to battle in Kursk, but as it looks right now, after some initial gains, the Ukrainian offensive is being rolled back. Elsewhere Ukraine also is trying to hold onto key towns, Chasiv Yar and Pokrovsk, by using additional troops to hold positions in both locations. It is too soon to know if the Russian advance, slow and plodding as it is, can be halted. But Ukraine is trying hard to reverse its multiple defeats on the battlefield and is now using its F-16s for the first time in support of front-line operations.

In all, Ukraine is trying to buy time and prevent a major breakout by Russia that could spell a rout for Ukraine's defenses. Zelensky's problem is two-fold: he is losing soldiers at a high rate, including allegedly thousands of deserters; he can no longer rely on huge deliveries of weapons from the US, which will inevitably further weaken Ukraine's fighting ability.
I do not think the Trump administration will make any big promises to Zelensky. In fact, there are now more than rumors that the administration wants elections in Ukraine, perhaps by this coming Fall, and while not saying so, they would like to see Zelensky replaced with a more flexible leadership. Naturally, Zelensky does not agree and says that elections would wreck the army.
While General Kellogg will prepare options for President Trump's consideration, many of the possible components of a deal with Russia are already clear (and various leaks to the press tend to confirm what the administration is thinking).
One option can be taken off the table altogether, unless it is somehow modified. That is the idea of stopping the fighting with a ceasefire. The Russians have made it clear that a ceasefire would allow Ukraine to rebuild its military and acquire a new, larger arsenal of weapons. A ceasefire in place is similar in theory to what was agreed twice (2014 and 2015) in the Minsk agreements. It did not work then and the level of trust is so low now that it is doubtful that the Russians would accept any promises, such as no further deliveries of arms to Ukraine.
The alleged US plan includes a recognition of Russia's conquests in Ukraine, although it isn't clear whether recognition means de facto acceptance of the status quo or if it means de jure agreement that the captured territories are legally part of Russia.
Under the now defunct Minsk agreements, Donetsk and Luhansk would have remained part of Ukraine and subject to (some) Ukrainian laws and administration, but would in some unspecified manner be autonomous with protections for the Russian-speaking population of these territories. It is clear that model has been superseded by Russia's annexations of these territories, which also include Zaphorize, Kherson and Crimea.
The Ukraine war cannot end unless the future of these territories is agreed in a way that the external and internal parties can accept for the long term.
It seems that the Trump administration is not averse to canceling future Ukrainian membership in NATO. Keeping NATO out of Ukraine is a key demand made by the Russians. There is a problem, however.
Zelensky has demanded that he needs security guarantees from the United States and 200,000 NATO troops to protect Ukraine if Ukraine can't officially join NATO. One can ask, what is the difference in practice if there are NATO troops in Ukraine (perhaps officially as peacekeepers) and security guarantees? In essence, this is exchanging one problem, NATO membership, with another, NATO soldiers and security guarantees.
One way out of the dilemma is some kind of buffer zone, so far only vaguely defined. Would the so-called peacekeeping force actually operate in the buffer zone or stay outside of it? How could a buffer zone be managed, and who would be in charge of it?
In the Minsk agreements, the Organization for Security and Cooperation in Europe (OSCE) was supposed to help keep the peace and prevent violations of the deal. The OSCE was a failure and is unlikely to play that role again. Today there are not many alternative candidates. Like the OSCE, the UN could provide some sort of monitoring role, although the UN performance elsewhere has been far from satisfactory.
There are many other issues surrounding the Ukraine imbroglio. Russia will want its cash reserves in European and American banks, returned (perhaps with interest). The seizure of Russian funds is likely a violation of international law, for what it is worth. Those assets are valued at around $300 billion, perhaps more. Interest gained on the seized Russian assets has been handed off to Ukraine.
Another issue of some consequence are the gas and oil pipelines. Nordstream, for example, was mostly destroyed by "unknown" parties. Can Russia, one of the shareholders in Nordstream, demand compensation?
In addition, there is the broader range of sanctions, including the banking and SWIFT system, blocking transit and deliveries of goods, and other restrictions that impact Russia. Can Trump offer the Russians sanctions relief, and can he get Europe to cooperate? Take note that General Kellogg is suggesting substantially increasing the sanctions now as a way to pressure Russia into a deal.
Internally in Ukraine there is the issue of protection of Russian speakers in cities and towns under Ukraine's control. Ukraine has passed cultural and religious laws that violate western democratic and human rights standards. Will a peace deal require Ukraine to repeal them?
It is unlikely that Trump will be able to get a comprehensive deal, given the complexity of issues and the reluctance of the EU and its chief sponsors (Germany and France) to back any arrangement that rewards the Russians. This suggests that the Trump team will likely seek to "move the needle" on a deal by setting up potential future solution mechanisms in exchange for ending the fighting, leaving the other issues for future negotiations. Even doing this is a rocky road, and while the Russians might be persuaded, they will want very strong and binding assurances on arms supplies to Ukraine, including especially long range weapons such as the US HIMARS and ATACMS and the British-French Stormshadow/SCALP EG.
It is unclear what Vance and Kellogg will bring home from Munich, other than being pressured to keep the war in Ukraine going. Trump will have to try and work with the Russians to see if there is a way forward, while watching his back because of his NATO partners.
When you say “Europe wants to continue the war” you mean the wafer thin topslice of Euro elites perched atop governments that are in free fall everywhere.
It is abundantly obvious that Russia never wanted this war and has been seking an exit since the beginning. This is wishful thinking, as the West is absolutely itching for a fight.
Meanwhile, as long as the American and european elite classes are not themselves personally affected, they have no problem for continuing the war. Once Ukraine starts really running low on warm live bodies we can expect the call to go out to Send In The Poles!
EDIT: also, nobody cares what europeans think or want, although the political class is all in for more war. Remember when the europeans were fantasizing about staying in Afghanistan after the Americans were looking to pull out? The joke was that NATO stood for "Needs Americans To Operate". Like a dog, a european needs a Master.