According to the Mail on Sunday, senior Tories apparently fear that President Trump could be turfed out before completing his term in 2020, or face defeat at the ballot box.
The president has so far enthusiastically backed a US-UK partnership, tweeting recently that his team were "working on a big and exciting trade deal".
One minister told the paper it was crucial for the UK that Mr Trump remains in office.
"Davis knows Trump is our best hope of getting a first-rate trade deal,’ said the Minister. ‘We need to make as much progress with the US as we can while he is still there. If he goes it will be a different story.’
Elsewhere a Cabinet minister told the Sunday Times: "There is a view developing that it looks increasingly likely that he will not reach the end of his tenure mainly due to the impeachment opportunities.”
It has also emerged that Mr Davis is planning a trip to the US to promote a future trade deal.
The Mail on Sunday claims that could upset supporters of Liam Fox and Boris Johnson, whose ministerial roles are involved with promoting the UK abroad, whereas Mr Davis is tasked with leading the Brexit negotiations.
