Rebel Tory MPs are “circulating a smorgasbord of names” to replace Liz Truss as Prime Minister, former Cabinet minister Nadine Dorries said on Thursday.
However, she told them that ousting Ms Truss, who has been Prime Minister for just 38 days, would be “a totally untenable position”.
She argued that MPs could not “foist” upon voters another PM without a General Election.
Ms Dorries tweeted: “MPs circulating a smorgasboard of names re who should replace Truss as PM are not taking into account the fact that they cannot foist upon the British public another Prime Minister that the public have not voted for.
“A totally untenable position. #backliz”
Former Culture Secretary Ms Dorries has previously appeared to suggest that there should be a General Election if Ms Truss wanted to ditch a swathe of policies agreed under her predecessor, Boris Johnson, who got his mandate to govern from the 2019 election.
Her comments came after Paul Goodman, editor of the ConservativeHome webite and a former MP, speculated that Penny Mordaunt could become Prime Minister, with Rishi Sunak back as Chancellor.
He stressed that Mr Sunak would struggle to “command a consensus among Conservative MPs” to be PM.
“Might he and Penny Mordaunt – who took a majority of the votes of Tory MPs between them in the leadership election – somehow team up? With her as Prime Minister?” he added.
“Tory MPs are floating the idea, and far stranger ones too.”
Earlier, a Cabinet minster issued an unprecedented warning to rebel Tory MPs that ousting the Prime Minister just over a month into her premiership would be a “disastrously bad idea”.
Foreign Secretary James Cleverly said any attempt to replace Liz Truss now would hit the economy and the party.
It comes after the PM received a hostile reception from some backbenchers during her first meeting of the powerful 1922 Committee as leader on Wednesday night.
One senior MP accused her of trashing 10 years of Conservative government with an unfunded tax cutting budget that spooked the markets and sparked a plunge in the value of the pound.
A growing number of Tory MPs have now begun to turn on the new prime minister as Labour surges ahead in the polls.
Mr Cleverly told BBC Radio 4’s Today programme: “We have got to recognise that we do need to bring certainty to the markets.
“I think changing the leadership would be a disastrously bad idea politically and also economically."
Chancellor Kwasi Kwarteng is now under pressure to reinstate a planned increase in corporation tax from April in an effort to reassure the bond market that there is a strategy to get public finances under control.
Mr Cleverly added that the Government would remain committed to cutting taxes, but refused to rule out raising corporation tax to help restore market confidence.
"We are absolutely going to stay focused on growing the economy," he said.
