The Times claims on its front page that senior civil servants have expressed fears Jeremy Corbyn is "too frail" to become prime minister.
It says the issue was openly discussed at a meeting of top officials this month, where doubts about the state of the Labour leader's physical and mental health were expressed.
The article quotes one unnamed mandarin who believes Mr Corbyn is being "propped up" by his advisers.
A Labour spokesperson said Mr Corbyn was in good health and that claims he did not make his own decisions were "laughable and demonstrably false."
The Daily Mail highlights a YouGov poll suggesting Jeremy Hunt is now more popular with voters than Boris Johnson.
It says 41% of those questioned would prefer the foreign secretary to become the prime minister, as opposed to 29% who back his Conservative leadership contest rival.
Amongst Tory voters, Mr Johnson leads by 48% to 39%.
The paper's editorial urged Mr Johnson to "ditch the circus act and get serious".
In the i, Andrew Grice says the poll shows Mr Johnson now "faces a real fight, not simply a coronation".
Writing in the Times, Janice Turner muses on the disparity between the wider public's opinion and Mr Johnson's popularity among Conservative members who will vote, noting that watching the contest as a non-member "is like being a child, powerless while an adult row rages above our heads".
The Daily Telegraph reports that George Osborne is considering a return to politics. It says the former Chancellor is "toying" with the idea of standing in the marginal Kensington constituency in the next election.
A source is quoted as saying that the editor of the London Evening Standard is "missing the cut and thrust" of politics, and has targeted the seat where Labour hold a majority of just 20 as an ideal route back into Westminster.
Some of the cartoonists have focused on the G20 summit.
The Daily Telegraph's Bob Moran has recreated the image of Theresa May shaking hands with Vladimir Putin which appears in most publications - but with the prime minister wearing a full chemical suit and a gas mask.
Ben Jennings also depicts the Russian president in the i, urinating on the Statue of Liberty's flame with Donald Trump, as Boris Johnson clambers up the monument's hand to join them.
Finally, the Daily Mirror has a story about a retired engineer from Las Vegas who looks set to become a millionaire thanks to owning the only surviving original recordings of the first moon landing.
Gary George bought over a thousand video tapes from Nasa in 1976 for just $218, with the plan to resell them to local television stations to tape over the material.
Sotherby's auction house estimates the tapes - which are clearer than any other footage of the event - could fetch over $2m (£1.6m) when they are sold in New York next month.