The six-time Ballon d'Or winner became a free agent when his contract at Camp Nou, where he has spent his entire senior career, expired at midnight on 30 June.
However, following months of speculation regarding Messi's future, Catalan dailies L'Esportiu and Sport reported on Thursday (AEST) that the 34-year-old has agreed to stay on.
An announcement could be made as early as Thursday, it is claimed, once LaLiga officials have signed off on the contract.
Barcelona is facing high-profile financial problems and need to reduce its wage bill if it is to comply with LaLiga's financial fair play rules.
Speaking on Monday, however, Barca president Joan Laporta revealed talks between the Catalan giant and Messi were "progressing adequately".
The same reports suggest Messi has agreed to a far lower salary, potentially as much as 50 per cent on his previous deal that was signed in 2017.
The five-year contract will take the superstar forward through to the age of 39, though Barca may allow Messi to see out the final part of his career in Major League Soccer.
Paris Saint-Germain and Manchester City were the main frontrunners for Messi last year, though neither club made an immediate move for the free agent.
Messi was again hugely influential for Barcelona last season, finishing as LaLiga's top scorer and managing 38 goals and 12 assists across all competitions.
Taking all competitions into account, he created 117 chances for others and netted a goal every 110.32 minutes.
Full-back Jordi Alba was next on the list of the most chances created for Barca in 2020-21, teeing up 85 goalscoring opportunities.
Despite the speculation surrounding his club future, Messi carried his club form onto the international stage by inspiring Argentina to their first Copa America crown since 1993.
He scored four goals and chipped in with five assists to win his first piece of silverware for his country.