Martial has expressed his desire to leave United in recent weeks after a lack of playing time in the last 18 months.
Interim manager Ralf Rangnick has confirmed United have turned down a loan offer from Sevilla, who only wanted to pay half of his wages.
ARA Esports have now claimed Barcelona are interested in the 25-year-old on a six-month loan - as long as Dembele goes the other way.
Dembele is in the final six months of his deal at the Camp Nou and negotiations over a new contract have stalled.
It's believed the France international is demanding an outrageous €40 million-per-year contract alongside a signing-on bonus of €20 million.
Dembele is free to negotiate with other clubs at any time and Barcelona's recent signing of Ferran Torres makes a new deal complicated.
Torres arrived from Manchester City in a €55 million deal on Wednesday and will be a key player in Xavi's new-look side.
Dani Alves' return means the Catalan giants have a number of players to register and want to shift some of their biggest earners.
Philippe Coutinho and Luuk de Jong are two other attackers that could depart within the next month.
Martial hasn't played under Rangnick and he confirmed there's currently no injury issue in a press conference.
Speaking ahead of Monday's game with Wolves, Rangnick admitted per Metro: "He made it very clear that he wants to leave and, in a way, I can understand his wish to leave and to try to play more regularly somewhere else.
"But it’s a question not only of what he wants to do but a question of which kind of clubs are interested in him and do they meet the demands of the club, so we have to wait and see.
"He is not injured currently so I decided to go for this group of players that were in the squad today, so it had nothing to do with injuries."
Cristiano Ronaldo and Jadon Sancho's arrivals in the summer have seen Martial slip down the pecking order at Old Trafford.
Mason Greenwood's emergence and Edinson Cavani's form has also limited him to just seven Premier League appearances this campaign.
Featured Image Credit: Manchester United & Alamy
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