Tories are jostling for position to succeed Theresa May, with a potential alliance between Boris Johnson and Amber Rudd seen by supporters as a way of bridging the party's Brexit divide.
The so-called Bamber – Boris and Amber – plan would see the Work and Pensions Secretary back Mr Johnson for the leadership in the hope that her influence would mean other MPs from the Remain wing of the party would follow.
Speculation about possible leadership contenders has heightened since Mrs May signalled she would leave office early if she could get a Brexit deal through.
The difficulties she has faced in achieving that and her decision to hold talks with Jeremy Corbyn have increased the pressure on her to stand down.
During the referendum battle, Ms Rudd said Mr Johnson was "the life and soul of the party but he's not the man you want driving you home at the end of the evening".
The Mail on Sunday and Sunday Times both reported on the potential "Bamber" tie-up, but said Ms Rudd had also considered the possibility of alliances with Michael Gove or Jeremy Hunt.
Asked about the "Bamber" rumours, Brexiteer Jacob Rees-Mogg said Mr Johnson could "unite the party and win an election" while Ms Rudd was a person of "first-class capabilities".
He told Sky News's Sophy Ridge on Sunday: "I think very highly of Boris Johnson, who managed to win in London twice in a Labour area – has a great connection with voters.
"He is a clear Eurosceptic but otherwise is very much in the middle of the Conservative Party.
"He is not particularly a factional character beyond the European issue and therefore I think could unite the party and win an election."
Mr Rees-Mogg said he also "thought highly of Amber Rudd" and "there will come a time, though we may find this difficult to believe at the moment, when there are other things to talk about than Europe, and at that point we will need all the talents that are arrayed within the Tory party, not just those of Brexiteers".
Andrea Leadsom, who stood for the leadership in 2016, did not rule out another campaign.
"I will be thinking about that when the time comes, but for now I'm supporting the Prime Minister to get Brexit through," she told BBC's Andrew Marr Show.
Asked what she had learned from the 2016 experience, the Commons Leader said it was "be prepared", adding that Leave campaigners had not been ready when David Cameron's resigned.
Treasury Chief Secretary Liz Truss, another potential leadership contender, said the Conservative Party needed to "reinvent" itself.
She said she was "not thinking about" the leadership: "I'm talking about ideas".
On BBC Radio 5 Live's Pienaar's Politics she said 2019 "should be a year where the Conservative Party really says 'what are we about, what does the future look like'?".
"I've set out where I think we should be going: popular free-market conservatism, lowering taxes, building more homes, boosting education.
"Other people have their views but let's talk about the ideas before we go headfirst into another leadership election and we end up not having aired that.
"The Conservative Party modernised itself under David Cameron in 2005 but that's a long time ago and we need to reinvent ourselves for where Britain is now."