Concerned about the welcome he would receive in the UK, the President is understood to be sending US Secretary of State Rex Tillerson instead.
The White House has yet to respond to The Independent's request for comment.
Downing Street declined to comment on the particular case but reports suggested No 10 was aware the "working visit" had been postponed.
Mr Trump had been due to come to London to open the new £750m embassy, but was said to have abandoned the idea as he feels unhappy about the scale of the visit and the arrangements made.
He is said to be unhappy about the lack of "bells and whistles" surrounding the event and the fact he would not be able to meet the Queen.
The President had reportedly been due to meet with Prime Minister Theresa May at No 10, with 26 and 27 February provisionally scheduled in the diary. Downing Street had hoped to firm up the dates this week, the Daily Mail reported.
The decision is in contrast to comments made by the US Ambassador to the UK, Woody Johnson, at the end of last year that Mr Trump was planning to visit in the new year, and comments by Ms May last week that he "will be coming to this country".
Ms May controversially extended the offer of a state visit when she became the first world leader to meet Mr Trump in the White House following his inauguration last year.
Since then, however, the President has indicated he does not want to take up the invitation if he is going to face mass demonstrations.
Last month Labour leader Jeremy Corbyn called for his supporters to go out in force to send Mr Trump a "clear message" that he is not welcome if he comes to the UK.
The opposition to his visit meant the original plan for an official state visit, which would include a chance for Mr Trump to meet the Queen, was downgraded to a "working visit" which carries much less prestige.
In addition, Ms May and Mr Trump fell out spectacularly in November over his retweeting of anti-Muslim videos posted online by the deputy leader of the far-right Britain First group, Jayda Fransen.
At the time, the PM said Mr Trump was "wrong" to retweet the videos, and the US president hit back at Ms May on Twitter by telling her to focus on "destructive radical Islamic terrorism" in the UK, rather than on him.
Additional reporting by PA