A US diplomatic source told The Telegraph: "There are plenty of chances to get the President over here. We are opening our new embassy soon."
The new US embassy in London, based near Battersea Power Station, is opening in January.
British and American officials insisted that the full state visit would still go ahead, with a trip expected by the end of 2018.
But the fact that Trump's first visit may now not include the pomp and ceremony originally envisioned will be seen as a climb down.
May hand-delivered the invitation of a state visit when she became the first world leader to visit Trump after his inauguration in January.
The move was designed to play on Trump's warmth towards the Royal Family - he has spoken of how his Scottish mother was a "big fan" of the Queen - and build links with the new President.
Golf at Balmoral Castle, tea at Buckingham Palace and a procession down Horse Guards Parade were all discussed when Trump's allies talked to Foreign Office officials in the months that followed.
However a backlash among MPs - more than 200 signed an early day motion opposing him addressing both Houses of Parliament - and the threat of mass protests saw the visit delayed.
May made no mention of the state visit in her Queen's Speech after the June snap election, as would be customary if a trip was imminent. She did mention a state visit for King Felipe of Spain, who came in July.
There had been reports that Trump was considering a brief visit to his golf courses in Scotland in July, but the trip never came about.
A more informal visit would require less preparation and help Trump avoid large scale protests that could follow his visit to the UK.
Downing Street declined to confirm the reports. A spokesman said: "We are working on dates for a state visit for President Trump but there are no updates. I am not aware of any other discussions."
Jeremy Corbyn, the Labour leader, jumped on the news by offering Trump a tour of a mosque in London to teach him about diversity.
A spokesman for Corbyn said: "We have said this state visit should not go ahead but Jeremy has said he would be happy to meet President Trump and take him to Finsbury Park Mosque.
"If Trump comes to the UK [for a working visit] Jeremy would meet him and would like to show him different communities."
A Foreign Office spokesman said: "Our position on the State Visit has not changed - an offer has been extended and President Trump has accepted. Exact dates for President Trump to visit have not yet been arranged."