The Old Etonian has seen his stock rise over the summer, becoming the second most popular choice to succeed May, according to a poll of party members and bookmakers’ odds.
The Prime Minister is seeking to tighten her grip on power, after being labelled ‘deluded’ after vowing to lead the Tories into next election.
According to The Times, May is looking to bring rebels into line as Brexit negotiations continue and she clings on to power, with a government propped up by the DUP.
Rees-Mogg has become an unlikely social media hit
A source said she is “bringing him in” to a role that would make him “do a bit of grind” in office.
“People have to earn their spurs,” a Downing Street source said in reference to Rees-Mogg’s suitability for the top job.
The source added: “It’s great to be the fun uncle who turns up to see the children, stuffs their mouths with McDonald’s, takes them on the rollercoaster, winds them up before bedtime and then walks away.
“The grown-ups have to deal with the consequences.”
According to the paper, Sir Patrick McLoughlin, the party chairman, may step down and be replaced by Boris Johnson.
The Times reports that senior sources believe May has lost patience with the foreign secretary, who has been widely criticised for his performance in recent weeks.
It also reports that May will delay the reshuffle and punish rebels. In recent months, she has clashed with the likes of Sajid Javid, the communities secretary, Andrea Leadsom, the Commons leader, and Liam Fox, the international trade secretary.
Last week, May dismissed criticism of her, insisting she “isn’t a quitter”.
Former ministers Nicky Morgan and Grant Shapp have said it would be difficult for her to continue following the disastrous election this year which saw her lose the Tory majority.
Jon Trickett, shadow minister for the Cabinet Office, said Mrs May was “deluding herself”.
At a press conference alongside Japanese prime minister Shinzo Abe, Mrs May said: “I said I wasn’t a quitter and there is a long-term job to do.
“There is an important job to be done in the United Kingdom, we stand at a really critical time in the UK,” she said.