The US President wants to make a high-profile trip to the UK and the Republic of Ireland as early as June, according to sources.
The possible re-introduction of a hard border between the two nations has been a major sticking point in Brexit negotiations.
But Donald Trump’s allies believe he could act as a “troubleshooter” to help find a solution to the thorny issue.
His proposed working visit would narrowly avoid a clash with Prince Harry‘s wedding to Meghan Markle at Windsor Palace on May 19.
It is widely believed Mr Trump has not been invited to the royal wedding, sparking fears of a diplomatic row with Washington.
But his hastily arranged visit would help heal any possible rift with Theresa May’s government over the embarrassing snub.
Mr Trump has already confirmed he will visit the Republic of Ireland after a meeting with Taoiseach Leo Varadkar last week.
He said: “I would love to visit Ireland soon, I will come, I love it, I have property there, I will go.”
Asked about the border between Belfast and Dublin, the President added: “That’s an interesting border.
“There are two interesting borders, it is going to be interesting as to what happens.”
Mr Trump also received a hand-delivered invitation to Northern Ireland during St Patrick’s Day celebrations at the White House.
An insider told the Sun on Sunday: “He absolutely loved it and wants to go as soon as possible.
“The letter came from a major figure in the Northern Irish community and it has made him even more enthusiastic to go as soon as possible.
“He’s on his travels in June so it possible that a visit could be squeezed in then.”
However, it is unlikely he would visit any UK Cabinet ministers or members of the Royal Family during his working visit.
But he is poised to met Theresa May and the Queen during an official state visit to London in the autumn.
The row over the future of the Irish border has repeatedly threatened to derail Brexit negotiations between the UK and EU.
Brussels has suggested a “backstop” solution in which Northern Ireland would remain economically tied to the Republic of Ireland.
But Mrs May has warned the EU that she would “never” sign any Brexit treaty that divided Britain and Northern Ireland.
In a speech last week, European Council president Donald Tusk warned the Prime Minister she must find a solution to the issue by June.