However, the Government refused to confirm that the trip would take the form of a state visit rather than a less prestigious working visit.
Following Ms May’s and Mr Trump’s joint conference at the World Economic Forum, a Downing Street spokesman said the two leaders reiterated “their desire for a strong trading relationship” after Britain’s exit from the European Union.
The spokesman added: “The PM and President concluded by asking officials to work together on finalising the details of a visit by the President to the UK later this year.”
A senior government source said the visit is likely to take place during the second half of 2018.
“Officials will talk about what type of visit and when it will be”, the source said. “The PM and the President agreed that they'll get their people and our people to talk about the plans and there wasn't any discussion beyond that.”
It comes after the Mr Trump cancelled his scheduled visit to Britain – originally pencilled in for February – amid fears of mass protests. But he also claimed he was not willing to open the new US embassy in London because his predecessor Barack Obama’s “bad deal” in selling the former building for “peanuts”.
It was not immediately clear whether the trip would be an official state visit – an offer extended to the President just days after he was inaugurated in January last year.
On Thursday, the two leaders fended off a barrage of questions about the state visit during their joint appearance, with Mr Trump saying “we’ll talk about it” when asked about a potential trip to the UK.
“We’re on the same the wavelength in, I think, every respect,” he said. “The Prime Minister and myself have had a really great relationship, although some people don’t necessarily believe that, but I can tell you, I have a tremendous respect for the Prime Minister and the job she’s doing.”
“I think the feeling is mutual from the standpoint of liking each other a lot,” he added as Ms May nodded in response. “There was a little false rumour out there. I wanted to correct it.”
The relationship between the pair has appeared rather rocky, with Ms May publicly condemning Mr Trump’s retweeting of several anti-Muslim videos posted online by a “hateful” British far-right group.
Mr Trump tweeted back: “@Theresa_May, don’t focus on me, focus on the destructive Radical Islamic Terrorism that is taking place within the United Kingdom. We are doing just fine!”
The Downing Street spokesman added: “The two leaders began by discussing Bombardier, with the PM reiterating the importance of the company’s jobs in Northern Ireland.
“The PM and the President discussed Iran, and the need to work together to combat the destabilising activity that it is conducting in the region, including ballistic-missile development, and continuing efforts to ensure Iran does not develop nuclear weapons.
“They also agreed on the importance of continuing to stand side by side in the fight against Daesh [Isis] in Syria and elsewhere.
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