The Conservative leadership candidate Esther McVey told Nick Ferrari that the Prime Minister will need only Brexit supporters around them in order to push through a plan to leave the EU.
That will be bad news for senior Remainers in the Cabinet such as Philip Hammond, David Gauke and Rory Stewart.
Speaking to LBC, she said: "I believe at the moment we actually have to have a team that believes in Brexit.
"They have to, because this is the most difficult delivery that we've got to give - and we've got to give it by the 31st October.
"You need to have people who believe in Brexit to deliver this by the 31st October.
"It would be a Brexit-only Cabinet until the 31st October."
Tory leadership contenders
Tory leadership contenders
Former Brexit secretary Dominic Raab at 'A Better Deal' event at the British Academy, London, outlining opportunities if Parliament rejects the Government's proposed deal, ahead of the House of Commons vote on the Prime Minister's Brexit deal.
File photo dated 10/01/19 of former foreign secretary Boris Johnson, who has breached House of Commons rules by failing to declare a financial interest within the required time limit, the Commons Standards Committee has found.
Conservative former minister Sam Gyimah who has become the 13th MP to throw their hat into the race to replace Theresa May as party leader, leaves the Sky studios in Osterley, west London after appearing on Sophy Ridge On Sunday where he announced his intention to run.
Environment Secretary Michael Gove speaking at the V&A Museum, London during the Step Up To The Plate event, where food giant Nestle and major supermarkets Tesco, Sainsbury's and Waitrose pledges to help halve food waste by 2030.
Foreign Secretary Jeremy Hunt leaves the cabinet meeting in 10 Downing Street, London.
File photo dated 03/05/19 of Home Secretary Sajid Javid, who will warn in a speech to senior security figures, that British nationals could be banned from travelling to the last remaining rebel enclave in Syria under new counter-terror laws.
File photo dated 23/04/19 of Health Secretary Matt Hancock, who announced that the care of every patient stuck on segregated wards will be independently reviewed, after a report suggested many vulnerable people are being failed.
British Conservative MP Mark Harper speaks in the Parliament in London
Former cabinet minister, Esther McVey, launches Blue Collar Conservatism at the Houses of Parliament in London today.
Andrea Leadsom arrives at her home in London, she has resigned, saying in a letter to Theresa May "I no longer believe that our approach will deliver on the referendum result".
Secretary of State for International Development Rory Stewart arrives for a cabinet meeting at 10 Downing Street, London.