According to Moises Llorens at AS, "doubts have now emerged" about the Argentinian's new contract and "the possibility of Messi not signing a new contract should not be ruled out."
Should Messi opt not to renew, Manchester City could offer Barcelona €400 million for their talisman and have already been in touch with Messi's camp.
Barcelona announced Messi would be staying at Camp Nou until 2021 in July, via their Twitter account:
However, the 30-year-old is yet to officially sign the new deal, although club president Josep Maria Bartomeu has said he is already playing under the new contract, per 8TV (via Sacha Pisani of Goal).
Messi has started the season in superb form, helping Barcelona remain unbeaten in the Champions League and La Liga.
Opta noted how it is his best start to a season ever in the Spanish top flight:
Despite Messi's failure to sign a renewal so far, it would still be a shock if he opted to leave Camp Nou, having spent his entire senior career at the club.
However, with his contract set to expire in the summer, there must be genuine concern at Barcelona, particularly as he will be able to speak to other clubs in January.
Meanwhile, Barcelona will have competition from PSG for Coutinho, according to Joaquim Piera at Sport.
The Ligue 1 side are unable to sign the Brazilian in January due to financial fair play regulations.
However, they will instead try to stop him moving to Camp Nou and attempt to bring him in next summer and, according to the report from Piera, PSG have "made contact" with Coutinho's representatives.
Barcelona have a "real chance" of signing Coutinho this January and must decide if they will go for it, particularly as they are keen to avoid a bidding war with PSG, which would raise the price.
After missing the start of the season due to injury, Coutinho has shown exactly why Barcelona remain interested in his services, and his effectiveness is highlighted by Opta:
Per Simon Mullock at the Mirror, Liverpool have warned Barca they will not sell Coutinho in January, even if the Blaugrana return with a new bid.
A January move for Coutinho looks unlikely, particularly as the Brazilian has already featured in the Champions League for the Reds and cannot play in that competition for another club.
However, PSG's acquisition of Neymar has demonstrated the club's financial power, and unlike Barcelona, they may well be able to present Liverpool with an offer they are unable to turn down.