The France international, who is still on the sidelines recovering from a serious knee injury, is currently in talks with Barcelona over an extension to his current deal, which expires next June.
However, there has still not been an announcement by the Catalan outfit, and as it stands, the World Cup winner would be free to discuss a pre-contract with Man United in January 2022.
According to Mundo Deportivo, Man United are actively 'courting' the 24-year-old and are hopeful that he will turn down the chance to commit his future to Barcelona.
The report claims that several sides are monitoring the situation, with Juventus also said to be admirers of the attacker, who moved to Camp Nou from Borussia Dortmund in August 2017.
Dembele, who could return from injury by the end of October, has scored 30 goals and registered 21 assists in 118 appearances for his current side in all competitions.