The Red Devils are in the market for a new wide attacker during the ongoing transfer window, with Borussia Dortmund's Jadon Sancho their top target.
However, Dortmund's refusal to lower their £108m asking price and subsequent public insistence that Sancho will not be sold this summer has forced United to consider alternatives.
Dembele is thought to be one of the players on their shortlist, and Spanish publication Sport reports that Barcelona would be willing to consider offers for the 23-year-old.
However, the Spanish giants are looking to recoup a large chunk of the fee they paid to sign him from Dortmund three years ago and would therefore demand €90m (£81.4m) from any potential suitors.
Barcelona recognise that such a deal would not be likely with the impact of the coronavirus lockdown still being felt and so are willing to loan Dembele out for a season, so long as the agreement includes an obligation to buy.
The Frenchman has not played a single minute of competitive football since November due to injury and was limited to only five league appearances in 2019-20.