The Sunday Times said the Old Etonian, who has seen a sudden upsurge in popularity, was "sounding out" friends about a possible challenge.
Jacob Rees-Mogg has denied claims he is considering launching a leadership bid to replace Theresa May.
Anglo-US academic Ted Malloch, meanwhile, claimed that Rees-Mogg had let slip his leadership ambitions during a private lunch.
And a friend of the MP quoted in the Sunday Times said Mr Rees-Mogg was "loyal to a fault" and would not do anything to "destabilise" Mrs May.
"I said it is unrealistic for me to go from the backbenches to being leader", he told the Mail on Sunday.
He added: "I think if I threw my hat in the ring, my hat would be thrown back at me pretty quickly".
When HuffPost UK spoke to Rees-Mogg in July, he was somewhat cryptic about the calls to run for the Tory leadership, simply laughing: "I don't think giving one's sixth child an unusual name is qualification for being prime minister". The news came after Rees-Mogg was voted the second-most popular choice to become the next Conservative leader in a poll by the ConservativeHome website.
They added however: "But should she stand aside. he is starting to look at some of his more ambitious peers and wonder what they have got that he hasn't".
The MP for North East Somerset also has the backing of a grassroots movement nicknamed "Moggmentum", with backers seeking to portray him as a right-wing alternative to Jeremy Corbyn.
But on Broadcasting House, and in comments to the two newspapers that covered his leadership prospects, Rees-Mogg declined to rule out standing as a candidate in the Tory leadership contest widely expected before the next general election. "It would be the end".