The 24-year-old is yet to play for the Catalan giants this term through injury, and there remains speculation surrounding the Frenchman, with his current deal due to expire next June.
Barcelona are believed to be in talks with the attacker over a new contract, with the club determined to keep him at Camp Nou on a long-term basis.
However, as it stands, Dembele would be free to hold talks with Man United in January over a possible move to Old Trafford at the end of June.
According to El Nacional, the 20-time English champions 'have already contacted' the France international's agents to start 'negotiating his future'.
Dembele has struggled with a number of injury problems since joining Barcelona from Borussia Dortmund in August 2017.
The former Rennes youngster has made 118 appearances for Ronald Koeman's side in all competitions, scoring 30 goals and contributing 21 assists in the process.