Boris Johnson could come under pressure over whether to grant Foreign Secretary Liz Truss or her demoted predecessor Dominic Raab access to the grace-and-favour mansion of Chevening.
Downing Street suggested on Friday that no decision had been made over who to give access to the 115-room holiday home in Kent, with the final moves in the reshuffle still to come.
But The Times reported that both Cabinet ministers have staked a claim to the country manor reserved for use by a senior minister.
Mr Raab was said to believe his new role of Deputy Prime Minister, which formalised a title he effectively held and was largely interpreted as a consolation prize, means he should be able to keep it.
The Chevening Estate Act of 1959 states that the Prime Minister decides the “nominated person” to occupy the 17th century mansion.
No 10 said there is not “one single post” that is entitled to use the Grade I listed building, though by convention access is usually bestowed on the Foreign Secretary.
“There is a long process in place for nominating the occupants of Chevening House and we will update in due course,” the Prime Minister’s official spokesman said.
“We will conclude the reshuffle and then we will get into the longstanding processes, like residences.”
The spokesman declined to be drawn on the prospect of Mr Raab and Ms Truss getting access to the home under a sort of time share.
Downing Street has not denied suggestions that Mr Raab resisted his change of roles during a tense conversation with the Prime Minister during which he was made Justice Secretary.
Though an incredibly important role, the Cabinet post is considered to be a downgrade from foreign secretary, which is one of the four “great offices of state”.
It would not be the first time senior ministers have tussled over access to the palatial estate.
Deputy prime minister Nick Clegg, then the Lib Dem leader, and the Conservative foreign secretary William Hague shared Chevening as a “joint tenancy” during the coalition government.
Mr Johnson eventually became the “prime nominee” to the mansion as foreign secretary in 2016 after bids from his Cabinet colleagues David Davis and Liam Fox.