L'Equipe says United have previously enquired about Dembele's availability, but the former Borussia Dortmund forward snubbed their approaches.
Dembele has since fallen down the pecking order at the Camp Nou, and this, coupled with reports he has spoken to Paul Pogba about a move to Man United, suggest he's had a change of heart.
Dembele is even said to be "enthusiastic" about the prospect of signing for the Red Devils.
But the update comes as Barcelona sporting director Ramon Planes poured cool water on speculation United have already made an approach.
"First of all, no negotiations with Manchester United at the moment," he said. "Completely deny that. He's a player we count on, we know his potential.
"We hope this year the team sees the best of him."