United made a deadline day bid for Dembele in October and remain keen.
Mundo Deportivo says while the Catalan giants have opened talks over a new deal, Dembele's representatives have been talking to other clubs.
United are among the clubs contacted by Dembele's people, having 'positioned themselves' to sign him next month either on loan or on a permanent deal.
But United are not the only club interested in the winger, with Premier League rivals as well as Serie A outfits also said to be keen.
Dembele plays predominantly on the right wing, which has been identified as a position that Ole Gunnar Solskjaer needs to strengthen.