But any Liverpool comeback, the paper adds, would be contingent on two things - Carroll accepting a role as an impact substitute, and undergoing a personalised medical programme.
The report says the £35m man, who is spending the season at West Ham United, has not done enough to convince the Hammers to sign him up full-time.
That might come as something of a surprise to those who watched the 24-year-old torment West Brom at the weekend with a powerful brace of goals, but he only has five goals in 21 appearances this season and has also battled with injuries.
West Ham have an option to buy as part of their loan agreement, but appear to be looking elsewhere, with Wilfried Bony rumoured to be the striker they want to lead the line next season.
Rodgers and Carroll are set to talk about his Anfield future, and if the target man agrees to a personalised fitness programme and a limited role within the team, he has a chance to resurrect his career with the club.
Tottenham are another club with a striker shuffle in mind – the Daily Star says that they are set to negotiate with Aston Villa over the £15m sale of Christian Benteke.
While Spurs know Villa’s bargaining position will be weakened if the Belgian’s club are relegated, the flip side is that he could be the subject of a bidding war, with several top clubs impressed by his performances this season.
In addition, the paper breathlessly adds, Emmanuel Adebayor could be on his way out of White Hart Lane, Jermain Defoe’s injury worries mean that Spurs would be prepared to sell him for the right price, while Leandro Damiao remains a target.
The Wayne Rooney to Paris Saint-Germain story remains on the back pages – The Sun boasts a ‘world exclusive’ that Zlatan Ibrahimovic wants him to join him in Paris.
“If he wants to be part of the best project in football then there is only one club to sign for,” Ibrahimovic reportedly said.
“Only he knows the decision he is going to make in the summer but the project we are trying to build here is clear.
“We are not content with being the dominant force in France, we want to be the top club in Europe as well.
“I can understand why the owners are interested in Rooney — he is in the top 10 of strikers in Europe.”
The Daily Telegraph, meanwhile, says that Barcelona, Real Madrid and Bayern Munich are all ready to swoop for Manchester City captain Vincent Kompany should the defender’s row with his manager escalate to the point that the Belgian wants out of the club.
Right then - you've now read a couple of hundred words about what’s in the papers without mention of Paolo Di Canio. Feels good, right? We're afraid that feeling of relief ends here, however.
As much as Di Canio fatigue is setting in, Paper Round's job is to tell you what’s in the papers, and many of the back pages are leading on his belated clarification that he is not, nor has ever been, a fascist.
End of the saga, then?
The Sun brings us Rio Ferdinand’s view on Di Canio – and he reckons the Italian is an ‘absolute idiot’.
Or at least, he did once – in his 2006 autobiography.
When you think about it, using quotes in a 2006 autobiography to counter a quote from 2005 dragged up again this week is actually strangely fitting.
Elsewhere the Daily Mail ask why the Italian was at the funeral of an Italian terrorist bomber, and why he has a tattoo of Benito Mussolini.
The Daily Telegraph, meanwhile, brands his appointment at Sunderland as the ‘most botched recruitment in Premier League history’, suggesting that this story will run and run – at least until there’s some football to play.
- Sports & Recreation