United are desperate to sign a right winger and they have searched the market in the last week for available talent as a deal for Jadon Sancho looks increasingly unlikely.
Dembele, 23, was once the most coveted forward in Europe and his rapid rise convinced Barcelona to part with a potential £144million for the former Dortmund winger.
However, a string of injuries and question marks over the Frenchman’s application have left him battling for his future at the club.
Dembele was an unused substitute in Barcelona’s 1-1 draw with Sevilla on Sunday night and Koeman admitted afterwards that the winger could leave the club in the next 24 hours.
Asked specifically about Dembele, Koeman said: ‘There are things that can happen but at the moment he is a Barcelona player.
‘There is one more day — players can enter or leave.’
United have agreed a deal to sign Porto full-back Alex Telles, while Edinson Cavani is also set to sign a one-year deal.
But it’s a right winger that is likely to be the biggest deal of the day, if the club can manage to pull it off.
Dortmund’s stance means United’s only likely way of signing Sancho would be to pay the club’s £108m asking price.
Whereas United have explored a loan deal for Dembele, though Barcelona would be open to selling for around £55m.