The source said both sides had been unable to arrange a date for 2017 and were now looking for dates in 2018.
There has been speculation Trump was deferring the state visit, an occasion filled with pomp that involves a banquet with Queen Elizabeth II, amid concerns that it would draw protests over his presidency.
Questions about the trip also arose after it got no mention in the Queen's annual speech to parliament in June, when it is customary for the monarch to list upcoming state visits.
But Trump confirmed he would be visiting Britain at the G20 in Hamburg, where he met with May, saying he "will be going to London". Asked when, he replied: "We'll work that out."
May has been derided for seeking to curry favour with Trump and has come under fire for inviting him for a state visit so soon into his presidency.
Opposition Labour leader Jeremy Corbyn, the smaller Liberal Democrats and the Scottish National Party have all called for the state visit to be cancelled, as have some from May's own Conservative Party.
The Speaker of the House of Commons previously said he was "strongly opposed" to allowing Donald Trump to address members of parliament during the US president's state visit later this year.
More than 160 of parliament's 650 MPs have signed a parliamentary motion opposing an address by Trump, citing the travel ban and his comments on torture and women.
A speech to both Houses of Commons and Lords has been a feature of many previous state visits, including one by Barack Obama in 2011.
More than 1.8 million people have also signed an online petition saying Trump should not make the state visit as it "could cause embarrassment" to the monarch.
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