The former chancellor is expected to launch a fresh bid for the top job after losing to Liz Truss over the summer.
Polling suggests Mr Johnson - who was kicked out of office by his own MPs three months ago - would be favourite to win a members' vote.
A close ally, Sir James Duddridge, said he had received a message from the former PM saying: "I'm flying back, Dudders. We are going to do this. I'm up for it." According to the BBC's running total of MPs who have gone on the record with support, Mr Sunak currently has 104 backers. He said he was "very confident" Mr Sunak would stand, adding: "I think the critical issue here is going to be the economy. Rishi had the right plan in the summer and I think it is the right plan now."
Mordaunt backer Conservative MP Bob Seely said "I think we owe the country a collective responsibility to apologise" and said he believes Ms Mordaunt has the best chance of providing "unity and leadership" within the party.