Spanish football expert Guillem Balague, however, says the proposed deal is far from finalized.
Balague told the BBC that in order to keep Messi, Barcelona will have to reduce its wage bill by around $240 million (€200 million) in order to meet La Liga's Financial Fair Play requirements.
Barcelona is negotiating directly with Messi's father and representative, Jorge Messi, but the two parties are yet to come to an "agreement on all the points of a very complicated contract," Balague says.
The 34-year-old has "not negotiated" with any other clubs, however, and is instead holding out for the right deal that will keep him at the club at which he has spent his whole professional career.
"Nobody expects any other resolution than Messi staying at the club," Balague said.
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Barcelona endured a topsy-turvy 2020/21 campaign following the appointment of Ronald Koeman as manager last summer.
However the Catalans produced a remarkable second half of the season, losing just three times in 28 games to finish third behind eventual winners Atletico and rival Real Madrid.
Messi finished the season as La Liga's top scorer for the eighth time in his career, having hit 30 goals in 35 matches.
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