Dembele joined Barca in 2017 for £ 135million after breaking onto the scene with Borussia Dortmund.
However, things did not work out in Catalonia for the 23-year-old, who made just nine appearances in all competitions last season after suffering a severe hamstring tear that forced him to suffer a surgical intervention.
New Barca boss Koeman has revamped his squad this summer, and it looks like he could leave the club.
There is increased competition for places on Barcelona’s attacking line.
The rise of young Ansu Fati made him a regular on the first team, while new signing Francisco Trincao was also added.
Philippe Coutinho is expected to have a second chance at Barca, having returned from a Champions League triumph on loan with Bayern Munich.
ESPN report that United have identified Dembele as a backup signing if they fail to get their hands on Jadon Sancho – which increasingly seems likely.
But instead of forking out big bucks on a player who has barely played in the past two years, it is believed he would prefer an initial one-season loan with an obligation to purchase.
Dembele hasn’t done much to improve his chances of changing Koeman’s mind after apparently arriving late for practice on Monday morning.
Marca claims the former Rennes driver was 15 minutes late at the Ciutat Esportiva Joan Gamper training complex.
Koeman is believed to demand a great deal of respect for deadlines and organization, and has ordered players to arrive at least an hour before the start.