Trump has been invited to make a coveted state visit, penciled in for autumn, but no dates have been set, amid political turmoil in London and fears that the US president would be greeted by mass protests.
Trump was already a deeply unpopular figure in Britain before he criticized London mayor Sadiq Khan when he was managing the response to a major terror attack.
Britain's Guardian newspaper group pored doubt over the trip Sunday, reporting that Trump told May in a phone call in recent weeks that he does not want to go ahead with a state visit until the British public supports him coming.
White House officials say few discussions about the trip have taken place and Trump's travel schedule is already filling up.
The president is expected to travel to Poland and Germany next month and has agreed to attend summits in the Philippines and Vietnam.
There have also been discussions about visit Japan and perhaps South Korea.
A senior administration official said May and Trump did not discuss the issue when they spoke by telephone on Friday, although they have on earlier calls.
A Downing Street spokeswoman said the invitation was still on the table, but offered no timeframe.
"We aren't going to comment on speculation about the contents of private phone conversations. The Queen extended an invitation to President Trump to visit the UK and there is no change to those plans."