Andy Burnham could hold his first meeting with Donald Trump within weeks after he vowed to lobby the US for more Ukraine support.
The PM said he is 'likely' to go to New York for the UN General Assembly next month and would make the case for Kyiv alongside other European leaders.
In an interview with Bloomberg, Mr Burnham said details were not yet 'fully confirmed' - with No10 insisting decisions are yet to be taken.
The visit would be his first to the US as premier, with all eyes on whether he can forge a bond with the volatile president.
Keir Starmer's initial encounter with Mr Trump was seen as an unexpected success, although relations later soured over his refusal to participate in the Iran war.
Mr Burnham chose to make his first foreign foray to Ukraine yesterday, reiterating the UK's 'unwavering' support.
Andy Burnham said he is 'likely' to go to New York for the UN General Assembly next month and would make the case for Kyiv alongside other European leaders
Mr Burnham chose to make his first foreign foray to Ukraine yesterday, reiterating the UK's 'unwavering' support. Pictured with Volodymyr Zelensky
Volodymyr Zelensky responded to the signal of intent by handing over what officials have called a 'goldmine' of battlefield data to help bolster British security.
Mr Burnham urged Ukraine's allies to send more interceptor missiles to Kyiv as Ukraine struggles under continued Russian bombardment.
Mr Zelensky has repeatedly pleaded for more US-made Patriot interceptor missiles in recent months as Kyiv's stocks have diminished.
At one point Mr Trump seemed to agree that Ukraine could manufacture its own version, but backtracked.
US supplies have been diverted to the Middle East since the outbreak of war with Tehran.
Mr Burnham told Bloomberg he felt 'really confident' the issue was 'fixable', but added: 'There are other players who could help in the mix who we have influence with.
'It's probably going to be a solution that involves a lot of layers and a lot of negotiation.'
World leaders are set to deliver statements at the UN General Assembly between September 22 and 28. It is unclear whether Mr Trump is going to attend, or whether Mr Burnham is considering making another stop in Washington.
Russia has sought to capitalise on Ukraine's shortage of interceptor missiles by stepping up strikes, killing at least 23 people and wounding more than 100 in the past three days alone.
During his bilateral talks with Mr Zelensky, Downing Street said Mr Burnham stressed the 'strength of unity' among coalition of the willing countries.
A No10 spokeswoman said: 'It had been an honest and productive conversation during the coalition of the willing, the leaders agreed, and it was clear the international community needed to step up and ensure Ukraine got the support it needed to defend itself from Russia's barbaric attacks going into the winter.
'The Prime Minister emphasised the strength of unity among coalition members and reiterated that there would be no change in the UK's steadfast support.
'That was further symbolised by the announcement that the UK had agreed that defence firm MBDA could release classified information on UK components for the long-range missile, Scalp, the Prime Minister said.'
Mr Burnham and Mr Zelensky have also signed an agreement to give the Ministry of Defence, working with selected British companies, access to Ukraine's 'Avengers' AI database, Downing Street said.
The deal is expected to help the UK learn from Ukraine's experience on the battlefield and develop AI-powered solutions to national security challenges in both countries.
Meanwhile, a Kremlin adviser has suggested UK factories producing drones for Ukraine could come under attack from 'unknown sources' after Britain agreed to share long-range missile blueprints with the war-torn country.
Former deputy foreign minister for Russia Andrei Fedorov told BBC Newsnight he could not '100 per cent exclude' the prospect of 'semi-military' action against Britain.
It is unclear whether Mr Trump is going to attend the UNGA, or whether Mr Burnham is considering making another stop in Washington
Mr Fedorov said 'sooner or later, there might be not only verbal, but maybe some visible reaction from Russia towards the UK'.
Asked to elaborate, he said: 'There are different discussions how it should look like – it might be so-called technical reaction, maybe some hackers attack from unknown source, not from official level of course.
'There might be different political steps and I cannot exclude 100% that there might be some semi-military, for example.'
Pressed to define 'semi-military' he said: 'For example, something might happen with enterprises, with the factories which are producing drones for Ukraine, etc etc.'
Asked whether this meant British factories in Britain being attacked militarily by Russia, the adviser said: 'They could be attacked, not by Russia, but by… from unknown sources.'