It comes after the Guardian reported Mr Trump called Prime Minister Theresa May to say he did not want to visit until he had support from the British public.
He was invited for the state visit by the Queen.
Mr Trump was criticised after attacking London Mayor Sadiq Khan over his response to the recent terror attacks.
Mr Khan had told the public they should not be alarmed at the increased police presence on the streets after the attacks on London Bridge and at Borough Market.
But Mr Trump then accused him via Twitter of making "pathetic excuses".
A Downing Street spokesman said: "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."
The Guardian reported that, according to a Downing Street adviser who was in the room, Mr Trump made a call in recent weeks in which he stated his reservations about the visit.
Mrs May is reported to have been surprised by Mr Trump's position.
A senior official in the White House told the BBC that "the president has tremendous respect for Prime Minister May" and that the subject of the state visit "never came up on the call".
Following the Guardian article, Labour leader Jeremy Corbyn posted a message on Twitter, welcoming the "cancellation" of the visit.
Liberal Democrat leader Tim Farron said Mr Trump was "clearly terrified of the British public".
He added: "He knows that the British people find his politics appalling and that they won't be scared to make their views known.
"Theresa May should be embarrassed that she was so quick to offer Trump a state visit. Now neither of them want to be seen with the other."
Mr Trump's own Twitter account, through which he regularly makes announcements, has not made any recent mention of the UK state visit.