Trump ally Ted Malloch said he went for a private lunch with the hard Brexiteer, who reportedly expressed interest in the role.
Mr Malloch said: “I was at a lunch with Jacob very recently and he indicated he would like to be considered for the leadership when the time comes.
“He did not mean now, but at some point in the future.”
Mr Malloch also urged the Tories to dump “weak” May in favour of “lion” Rees-Mogg.
He told the Mail on Sunday: “The Conservative conference should make a bold move for new, fresh and even ‘cool’ leadership.
“This administration is weak and poorly governed. Its presently disabled leader should be replaced sooner, not later.”
Mr Malloch also attacked the former London mayor Boris Johnson, claiming the Conservatives needed “a charismatic and articulate leader who knows policy inside out, not a buffoon”.
Mr Rees-Mogg confirmed his meeting with Mr Malloch, and refused to rule out a tilt at the Tory leadership one day.
The North East Somerset MP said: “I said it is unrealistic for me to go from the backbenches to being leader. I am not a Cabinet Minister so it is hard to see how I could be a candidate. It is improbable bordering on impossible.”
He added: “‘There is no formulation of words I could use that would satisfy people but it is just not going to happen.
“It’s got nothing to do with me or my ambitions – it’s to do with political reality. I am not delusional.”
Mr Rees-Mogg did add “it’s in the interests of the country that she remains in office with the full backing of the Conservative Party”.
Mr Rees-Mogg has seen a groundswell of social media support in the wake of the snap general election, with a fan group known as “Moggmentum” calling for him to become the next PM.
Since being set up in June, one Twitter account associated with the “grass roots movement” already has nearly 8,000 followers.
Mr Rees-Mogg has also gathered a large following on Instagram, posting pictures of his family with…