Mr Hunt, the MP for South West Surrey, has already served as health secretary, culture secretary, and foreign secretary. The offer of being chancellor, another great office of state, could tempt him into Government.
It is a more senior post than defence secretary, which he turned down after his defeat in 2019.
But Mr Hunt, who is seen as being on the liberal wing of the party, has positioned himself as an “anti-Boris” candidate and he could therefore see political advantage in rejecting such a request and staying on the back benches.
Mr Johnson, who backed Brexit, beat Mr Hunt, who voted to stay in the EU, by 66 per cent of votes from party members to 34 per cent to claim the Tory leadership in July 2019.
Mr Johnson on Tuesday night expressed hope that the Tory infighting had eased as he spoke at an event marking the 40th anniversary of the Falklands War. The Prime Minister said: “Now things are a bit quieter in Westminster, perhaps I may be able to go before too long. Things seem relatively peaceful.”