The 30-year-old was in solid form for the Catalan giants during the 2020-21 season, scoring 19 goals and provided 12 assists in 49 games in all competitions.
Griezmann has been battling consistency since arriving from Atletico Madrid in 2019, however, he was linked with a move away from Camp Nou last summer.
According to Calciomercato, Barcelona will be ready to allow the World Cup winner to advance to the next transfer market if the right gift arrives.
Barca are struggling financially, and the club is thought to be prioritizing the actions of free agents, including Sergio Aguero, Eric Garcia, and Memphis Depay, this summer.
Griezmann, who has scored 34 goals and 16 assists in 97 games for Barca in all competitions, has more than three years left on his contract at the Camp Nou.