According to the Mail on Sunday, Theresa May will make a grovelling apology at the Conservative Party conference for the loss of the government's majority, to try to head off a threat to sack her as prime minister.
The paper calls it her "mea culpa".
In an editorial, the paper says it is right that Mrs May will show contrition - but adds that the time for apologies is over.
It says decisiveness and clarity are the best way of uniting the cabinet, her party, and ultimately, the country.
The Sun on Sunday, meanwhile, says Mrs May is being urged to clear out what it calls the "Brexit-bashers" in a mini reshuffle in order to reassert her authority.
The Mail believes Chancellor Philip Hammond and the Scottish Tory leader Ruth Davidson are poised to back a leadership bid by "soft-Brexit" supporter, Home Secretary Amber Rudd - if Mrs May is forced to step down.
Although when asked directly about his ambitions, he told the Sunday Times: "I think if I threw my hat into the ring, my hat would be thrown back at me pretty quickly."
In an editorial, the paper says what it calls "Moggmentum" is gaining strength.
"Could he become Tory leader? Stranger things have happened", it concludes.
The Observer has an article by the former Labour Foreign Secretary David Miliband calling for politicians on all sides to fight back against what he calls the "worst consequences" of Brexit.
He says the country should have the chance to vote on any Brexit deal in a second referendum with a straight choice between remaining in the EU and the negotiated alternative.
The former Business Minister, Anna Soubry, who campaigned for remain in the referendum, says a hard Brexit would destroy the lives and livelihoods of her constituents.
In the Mail on Sunday, she says "it's not impossible" that she could join with like-minded people who wanted to save the country from that fate.
In the Sunday Telegraph, Chancellor Philip Hammond, and the International Trade Secretary Liam Fox have written a joint article insisting the UK will leave the customs union and single market when it withdraws from the EU.
They previously appeared to have opposing views on Brexit.
The ministers stress there should be a limited transition period but say this must not be a means of staying in the EU.
Five pages of the Mail on Sunday are given over to the first hand account of the British model who says she was abducted in Italy by masked men, who wanted to sell her as a sex slave.
It says Chloe Ayling has given her first account of her ordeal.
The paper says her story has divided the nation and invites its readers to decide whether she was telling the truth.
The Sunday Mirror has spoken to her agent, who says police posed as him in an effort to track down her captors.
The Daily Star Sunday is predicting a Royal wedding. It says Prince Harry's inner circle claims he has asked his actress girlfriend, Meghan Markle, to be his wife - adding that she has accepted.
The People says Ms Markle has received her first seal of approval from the royal family - from Mike Tindall, the husband of Prince Harry's cousin, Zara Philips.
It quotes the ex-England rugby union international as saying Ms Markle will do "absolutely fine" if she becomes a royal - even though he has not actually met her yet.
The success of Great Britain's men in 4x100m relay at the World Championships came too late for the first editions of Sunday's papers.
But Sir Mo Farah is pictured on many front and back pages - the disappointment at coming second in the 5,000m final clearly shown.
The Sunday Times is kinder, saying that if defeat is the making of a true champion, then Farah left the track as the greatest champion of all.
The Sunday Telegraph sums up his legacy as: "A loser on the night, a winner forever."
David Kidd, the Sun on Sunday's chief sports writer, says even the greatest icons are eventually caught by an invincible opponent - old father time.