Separately, Trump's tweets about London Mayor Sadiq Khan in the aftermath of the London Bridge terrorist attack drew condemnation from across the British political spectrum, prompting Khan to call on the British government to cancel Trump's visit.
It is thought Mr Trump could make a surprise visit to his golf course near Aberdeen or another in Turnberry.
But the decision leaves open the possibility of a low-key visit to London before the end of this year if Mr Trump is in Europe on other business.
The White House did not respond to a request for a comment.
The President said during the G20 summit in Hamburg last weekend that he and the Prime Minister had developed a "very special relationship". The visit was originally planned for this fall, according to multiple reports.
"I think it's wholly right that the president should come".
Senior British politicians, including Labor leader Jeremy Corbyn and former Liberal Democrat leader Tim Farron, who called Trump "an embarrassment to America", said the visit should not go ahead.
The mayor of London, Sadiq Khan, clashed with Trump over the immigration measures, later saying the United Kingdom should not "roll out the red carpet to the President of the U.S. in the circumstances where his policies go against everything we stand for".
She invited him to visit the United Kingdom with the full pageantry of a state visit - which usually includes a banquet with the Queen and speech to Parliament.
And after the state visit was dropped from the Queen's Speech, there was speculation it might never take place at all.