The chancellor insisted he remained a loyal ally of Mr Johnson, despite publicly urging him to stand down amid a flurry of ministerial resignations last week.
“Boris Johnson is a friend of mine for 30 years,” Mr Zahawi told LBC on Wednesday. “If he wishes to serve in cabinet then I would certainly offer him a job.”
He added: “He has been probably the most consequential prime minister of his generation. He’s delivered Brexit.”
Mr Zahawi, one of the eight candidates who made in onto Wednesday’s first round ballot after receiving 20 nominations, is at pains to point out to Johnson loyalists that he did not betray the PM.
Many of the junior ministers who stayed in government and MPs who accepted ministerial roles last week amid the turmoil of the rebellion are angry at Mr Sunak over his perceived “treachery”.
Mr Zahawi explained why he called for Mr Johnson to go on Thursday, having accepted the role of chancellor only two days before. He said he wanted to “put country first”, but realised on Wednesday “we couldn’t realistically have a functioning government”.
“I went to Boris Johnson [on Wednesday] and explained he was in danger of being humiliated, and I didn’t want to see him being put through that,” he told BBC Radio 4’s Today programme. “He’s a friend of 30 years.”
He added: “The next morning. I felt the only thing I could do was write a letter to him, to remind of our conversation and ask him to do the right thing. And I think he did the right thing ultimately.”
It come sas Jacob Rees-Mogg said he would refuse to serve in Mr Sunak’s government because loyalty was “extremely important” to him.
The Brexit opportunities, who is backing Liz Truss, said she had “opposed the endless tax rises of the former chancellor, which I think have been economically damaging”.
Asked how long Ms Truss had been planning a leadership campaign, Mr Rees-Mogg responded: “She may have had drinks with MPs and meetings, but that’s the routine business of cabinet ministers. Even I had drinks parties with other MPs – when I was allowed to.”
Referring to Mr Sunak’s team registering his campaign website back in December – as first reported by The Independent – he added: “It’s not setting up a website, it’s not getting ready in December … that’s a different order of magnitude.”
Asked if he would take a cabinet post from Mr Sunak if became PM, Mr Rees-Mogg said: “No, of course I wouldn’t. I believe his behaviour towards Boris Johnson, his disloyalty, means I could not possibly support him.”
Mr Sunak has been subjected to bitter attacks from Johnson loyalists, with Mr Rees-Mogg accusing him of being a “socialist” chancellor and Nadine Dorries claiming he has waged “dirty tricks” to ensure he wins.
Tory MP Mark Francois, chair of the European Research Group (ERG) of Brexiteers, has said he is backing Liz Truss for the leadership.
“I have personally decided to vote for Liz Truss to be our next prime minister,” he told The Telegraph, hailing her “experience and leadership ability to unite the Conservative Party”.
The group of around 60 MPs in the group is set to meet at midday to discuss the candidates, but it is not clear they would agree on one candidate. Steve Baker – the self-declared “Brexit hardman” and former ERG chair – is backing Suella Braverman.