The Argentina international has two years left to run on his current deal at the Camp Nou.
ESPN FC has reported that he will be offered his 10th contract with the club since first penning a professional deal in 2004.
Barça president Josep Maria Bartomeu will meet Jorge Messi, the forward’s father and agent, for negotiations.
There is currently a clause in Messi’s contract to extend his terms by a further year, but the Barcelona chief wants to agree a fresh deal that will keep the Argentine in Catalonia for four more years.
Messi is already the world's highest-paid player with a salary of £64m per year at Barça.
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