Slack also said the invitation of a state visit for Trump, made in January, still stands. Opponents of the U.S. president have called on Theresa May to scrap plans for an official state visit, promising mass protests in response.
The President's schedule could allow a flying stop as he crosses the Atlantic on his way to Bastille Day celebrations in France on 14 July.
White House Press Secretary Sean Spicer later denied this as false, especially since the stories indicated the president was anxious about possible protests against his presence by the British public, but the news eventually gave way to Trump's latest scandals.
Trump would be expected to come to Downing Street to meet the prime minister for informal talks as part of any such visit - though final confirmation would be likely to be given with just 24 hours' notice, to minimise the risk of disruption.
It's unclear whether he will return to the USA before travelling to France the following Friday, but the Guardian reports that Whitehall sources believe Trump could visit one of his golf courses in Scotland during the interim.
News of the potential visit put protesters on "standby" with several prominent lefties urging people to march against the Republican leader.
"But we'll oppose him whenever and however he comes to the United Kingdom", said Nick Dearden, director of Global Justice Now, a Stop Trump coalition member. "Let's take to the street in great number - and do ourselves proud by showing that Britain rejects his hatred".
His golf club in New Jersey will host the U.S. Women's Open in two weeks.
May invited Trump to Britain seven days after his inauguration when she became the first foreign leader to visit him in the White House.
CNN has reached out to the White House for comment.