The 24-year-old has struggled with a number of fitness issues since making the move to Camp Nou from Borussia Dortmund in August 2017.
Dembele has only featured twice for Xavi's team this season, having picked up a hamstring issue after recovering from a long-term knee problem.
The World Cup winner featured against Benfica in the Champions League on Tuesday, but his future at Barcelona remains unclear, with his contract due to expire next June.
Man United continue to be strongly linked with the attacker, and according to El Nacional, the 20-time English champions still want to sign him despite his injury problems.
The report claims that potential new Red Devils boss Mauricio Pochettino is also behind the signing next year.