Joe Biden has played down the chances of brokering a post-Brexit free trade deal with the UK, as he held talks with Boris Johnson at the White House.
Downing Street said its priority was still getting a deal with the US alone.
But the BBC understands that UK ministers are now considering joining an existing North American trade pact instead of pursuing a separate deal.
The two leaders also discussed Northern Ireland, climate change and Afghanistan during the 90-minute meeting.
Downing Street said they “had agreed to continue working towards a future full free trade agreement”.
However, Mr Johnson had earlier also downplayed chances of securing a deal with the US before the next general election, saying: “The Americans do negotiate very hard.”
Speaking to reporters in the Oval Office before the talks, Mr Biden said the pair would discuss trade “a little bit”, adding: “We’re going to have to work that through.”
A deal would encourage trade by making it cheaper – usually by reducing or eliminating taxes called tariffs.
A source familiar with the government’s thinking suggested to the BBC that the UK could negotiate entry into an existing trade arrangement between the US, Canada and Mexico – known as the USMCA – set up after former US President Donald Trump tore up its predecessor, NAFTA.
“There are a variety of different ways to do this,” the source said. “The question is whether the US administration is ready. The ball is in the US’s court. It takes two to tango.”
Elsewhere, Downing Street said Mr Johnson and Mr Biden agreed all diplomatic and humanitarian methods must be used to stop conditions getting worse in Afghanistan.
The leaders said any international recognition of the Taliban must be contingent on the group respecting human rights.
It comes amid a request by the Taliban to address world leaders at the United Nations summit in New York this week.
Before the meeting, Mr Biden also issued a fresh warning to the UK that peace in Northern Ireland must not be jeopardised as a result of complications caused by Brexit.
Mr Biden made it clear he has concerns about the Irish border, amid continuing issues with Northern Ireland Protocol – the arrangement which helps prevent checks along the border between Northern Ireland and the Republic of Ireland.
The pair also discussed the new UK, US and Australia security pact in the Asia-Pacific, with No 10 describing it as an example of “shared values and approach to the world”.
The meeting – taking place on the sidelines of the UN summit – also involved the traditional exchange of gifts.
Mr Biden gave the prime minister a framed photo of their first meeting in Cornwall at the G7 summit in June, and a White House branded watch, according to officials.
Mr Johnson gave the president a signed copy of a book written by British astronaut Tim Peake with an inscription expressing hopes that it “provides a reminder of what we’re fighting to save as our countries tackle climate change together”.
The prime minister’s gift comes weeks ahead of the COP26 climate summit, which is seen as a crucial moment to bring climate change under control.
Earlier, Mr Biden announced the US would double its climate finance pledge and increase funding for developing countries to $11.4bn (£8.3bn) by 2024.
Mr Johnson said the US had “stepped up to the plate” with what he called a “massive contribution” towards the $100bn goal for countries to raise. bbc