The Brexit Secretary’s allies are said to be speaking with young rising stars in the Tory party with a view to replacing Mrs May before the next General Election, scheduled for 2022.
Under the plot, revealed by The Sun, Mr Davis would take the helm “for a few years” before handing over power to the next generation of Conservative MPs.
His supporters are said to be citing Mrs May’s difficulty in wrapping up the first stage of Brexit negotiations as a reason to push her out.
The paper reported a key ally of Mr Davis as telling one of the young Tory MPs: “Theresa has the smell of death around her.
“She’ll be gone by Christmas. It’s time to rally around DD.”
In an attempt to rally support for the plot, former Chief Whip Andrew Mitchell – one of the Brexit Secretary’s closest allies – is reportedly organising soirees with the next generation of Tory MPs.
The aim is to put together a “dream ticket” of newly elected Conservatives.
And two of the new MPs reportedly invited to an evening do last week, Tom Tugendhat and James Cleverly, have both been touted as future party leaders.
But one younger MP, who attended the get together with Mr Davis, told The Sun: “It was all very cloak and dagger, and I wasn’t very impressed by any of it.
“We just wondered what we were all doing there.”
The PM has faced a difficult week both at home and abroad, juggling the ongoing Brexit negotiations with attacks from within her own party.
Mrs May and her team seemed to be on the cusp of securing a deal on key divorce issues on Monday, but their efforts were undone after a last-minute intervention from the Democratic Unionist Party (DUP).
After wording of a draft agreement on the Northern Irish border leaked from the negotiations, the DUP issued a furious response objecting to the PM’s plans for “regulatory alignment” across the island of Ireland.
Then after returning to the UK, Mrs May was criticised by several prominent Tory Brexiteers during Prime Minister’s Questions.
Jacob Rees-Mogg asked: “Before she next goes to Brussels, will she apply a new coat of paint to her red lines?
“Because I fear on Monday they were beginning to look a little bit pink.”
But signs from Brussels, Stormont and Dublin tonight point towards a possible deal on the Irish border tomorrow.
A spokesman for Jean-Claude Juncker said an “early meeting is possible” between the EU Commission President and PM.
And European Council President Donald Tusk announced today he would make a statement on Brexit early tomorrow morning, furthering speculation a breakthrough could be imminent.