Last month, a date appeared to be set: Trump would head to London at the end of February for the opening of the new USA embassy.
The new United States embassy in London is located in a former post-industrial wasteland on the south side of the River Thames - a world away from its historic home in the capital's luxurious Mayfair district.
The ceremony may instead be hosted by US Secretary of State Rex Tillerson, sources in the US government suggested.
The comments came after US-UK relations hit a low at the end of past year when Trump retweeted anti-Muslim tweets from a member of a far-right British group.
The new embassy was designed by Kieran Timberlake architects is moving from Grosvenor Square to its new home overlooking the Thames from the south bank.
In a controversial move, May had extended the offer of a state visit when she became the first world leader to meet Trump in the White House following his inauguration previous year.
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Matters got even worse when Trump re-tweeted video posts of a British ultra-rightist group targeting Muslim immigrants in November.
Trump's ambassador to London, Woody Johnson, subsequently insisted: "The president and the prime minister have a very, very good relationship".
The US embassy is moving from Grosvernor Square in Westminster to the Nine Elms area of Wandsworth.
Here are some things to know about the new building, which opens to the public on January 16.
The latest development followed reports that Mr Trump wanted to delay a potential visit amid concerns about large-scale protests. London Mayor Sadiq Khan said Trump finally got the message that he was unwelcome in the U.K, which is why he canceled his visit.
Mr Trump was also scheduled to hold talks with Mrs May in No 10, with February 26 and 27 marked in the diary.
A petition to stop Trump from making an official state visit to Britain garnered over 1.8 million signatures past year, in a backlash over his controversial travel ban.