The 24-year-old's current deal at Camp Nou is due to expire next June, and Barcelona are believed to be finding it difficult to sign him to an extension due to their financial problems.
A recent report claimed that Man United view the France international as one of their 'main objectives' for next year, with new interim boss Ralf Rangnick also believed to be an admirer of his talents.
Barcelona will continue to work on a new deal, but the Catalan outfit will have a decision to make in January if they are unable to convince the former Rennes youngster to pen an extension.
Here, Sports Mole looks at how Man United could line up in the second half of the 2021-22 campaign if they manage to pull off a January deal for the attacker.
Dembele has played as a right-sided attacker for the majority of his professional career, but the Frenchman is also more than capable of operating off the left, and he has actually scored 11 times and contributed six assists in 39 appearances as a left-sided attacker for Barcelona.
Jadon Sancho has now scored in back-to-back games for Man United and looks to be making the right-sided position his own, meaning that Dembele could feature on the left for the 20-time English champions.
Cristiano Ronaldo was named on the bench against Chelsea on Sunday, but the Portugal international will still be a vital player for the Red Devils under Rangnick and will unquestionably start more matches than not in the second half of the 2021-22 campaign.
Fred, Scott McTominay and Bruno Fernandes are three players that should benefit from Rangnick's arrival, while Aaron Wan-Bissaka, Luke Shaw, Harry Maguire, Raphael Varane and David de Gea will all hope to be included in the first XI when they are available for selection.
Rangnick is spoilt for choice in the forward positions, with Marcus Rashford, Anthony Martial, Paul Pogba and Jesse Lingard among those capable of playing off the left, but Dembele could make that position his own if he were to make the move to Old Trafford in 2022.