Messi's deal at Camp Nou runs until 2021, but sources have told ESPN FC that Barca president Josep Maria Bartomeu has already initiated talks over a new lifetime deal.
Andres Iniesta signed a similar deal with the club in 2017, only to leave for Japanese side Vissel Kobe less than a year later.
Barca do not expect Messi's departure to be imminent, though, despite the forward using his acceptance speech at the Theatre du Chatelet in Paris to suggest he doesn't know how much longer he has left at the top level of the game.
"I'm aware of how old I am," Messi said after winning the Ballon d'Or for a record-breaking sixth time. "And I enjoy these moments so much because I know that retirement is approaching. Time flies."
Messi later added some nuance to his comments by saying that he still feels in great shape.
"I hope, God willing, that I keep playing for many more years," he told reporters after the Ballon d'Or ceremony when asked about retiring. "I'm now 32, though, and will be 33 at the end of the season, so, as I said, everything depends on how I feel physically.
"Right now I feel better than ever on a physical and a personal level, and I hope I can go on for a lot longer."
There is a clause in Messi's contract that would allow him to leave for free at the end of the season, should he wish. He allayed fears that he is about to walk away from Barcelona, though, by saying the small print in his contract is not important.
"Barca knows me and knows there's no type of problem with these issues," he said. "[My commitment] goes beyond a contract. What I feel for this club is [worth] more than any signature on a piece of paper, so there's no issue."
Eric Abidal confirmed last month that moves were being made to hand Messi