He insisted he was not "personally ambitious" and said he was not aware of a £750,000 war chest reportedly raised by supporters for an eventual leadership bid.
Pressed over whether he could put himself forward as a candidate for leader, he said: "There isn't a contest.
"I am technically eligible to become Pope, which is open to all Catholic males, but the College of Cardinals has not elected a non-cardinal since, I think, Urban IV.
"I'm very unlikely to be the next Pope and I'm very unlikely to be the next Prime Minister, for exactly the same reason. Though technically eligible, it is not the way history will go."
He joked: "The papacy would be fantastic. I would be infallible, which is better than is given to most politicians."
Speaking in a podcast for ConservativeHome, Mr Rees-Mogg named Home Secretary Sajid Javid and Environment Secretary Michael Gove as "first-class candidates" to succeed Theresa May when there is a vacancy.
And he appeared to tip Mr Javid as the more likely choice, noting that, during periods in power, the Conservative Party has always chosen a former chancellor, home secretary or foreign secretary as its leader.
Asked if the party might depart from that tradition, the North East Somerset MP said: "It's very unlikely, because Sajid has shown so successfully in his relatively brief period as Home Secretary that holding the seals of office means you can get things done, and that gives you an ability to show people what you can really do, and I think that's been so important for him."
The Home Secretary topped a regular ConservativeHome survey of Tory activists' preferred future leader for the first time earlier this week, ahead of Mr Gove. Mr Rees-Mogg dropped to third place after leading the field for the previous five months.
Mr Rees-Mogg said he was "not convinced I should be in the list at all", adding: "Both Sajid and Michael are first-class candidates and I have the highest regard for both of them.
"The Conservative Party in office has always, since (1920s leader Stanley) Baldwin, elected a former chancellor, home secretary or foreign secretary."
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