Penny Mordaunt has refused to drop out of the race and support Boris Johnson, sources have said.
According to reports, Ms Mordaunt refused and is said to have warned that most of her support would switch to Rishi Sunak if she did.
Earlier, former Home Secretary Suella Braverman announced her support for Mr Sunak to be the next Prime Minister.
In an article for The Daily Telegraph, Ms Braverman said she believes Mr Sunak is the only candidate who can unite warring factions within the party.
Going further, she said now is not the time for “fantasies” and urged her colleagues not to be “naive” when choosing who should lead the country.
Adding: “I need a leader who will put our house in order and apply a steady, careful hand on the tiller. That person, for me, is Rishi Sunak.”
According to Sky News, Mr Sunak has 136 MPs who have publicly backed him, Mr Johnson, 57, and Penny Mordaunt, 24.
