But the Guardian has since reported the embassy's plan to move from Mayfair to Nine Elms in London was first mooted in October 2008 when George W Bush was still president and Mr Obama had not yet been elected.
The President had also been due to meet the Queen in a full state visit at a later date but a source claimed the lack of "bells and whistles" may have put him off.
A design competition will ensure the new facility reflects the best of modern design, incorporates the latest in energy-efficient building techniques, and celebrates the values of freedom and democracy. The President is understood to be sending US Secretary of State Rex Tillerson instead.
But their relationship has soured after May criticised Trump's retweet of anti-Muslim propaganda from UK-based far-Right group, Britain First.
Any possible first trip to the United Kingdom by Mr Trump since being elected to the White House is likely to be met with fierce protests.
The US President was due to make his first trip to Britain since being elected a year ago, however he took to social media to say the date was off.
But large protests are expected to accompany any presidential visit to the British capital, where Trump is deeply unpopular.
Previous reports suggest that the construction of the new embassy was completely funded "by the sale of other properties in London". "We'll be going to London", Trump told reporters.
Theresa May insisted last week that Mr Trump "will be coming to this country".
Trump faced fresh criticism on Thursday night after the Washington Post reported that he had questioned planned changes to immigration rules, asking colleagues why the U.S. had to welcome arrivals from "shithole countries".
PHOTO: British Prime Minister Theresa May is pictured with President Donald Trump at The White House on January 27, 2017 in Washington.