Dembele joined Barca from Borussia Dortmund last year but spent much of the season struggling with a thigh injury that ruled him out of the team between September and December.
Since returning to the fold he has managed three goals and six assists in La Liga but Barcelona manager Ernesto Valverde is apparently unconvinced by the Frenchman and could seek to loan him out next season - or sell permanently, if the price is right. Liverpool have been one of those linked with a move in recent weeks.
Journalist Roger Sapares, who works for Catalan radio station RAC1, has revealed that Barcelona are testing the water to see if there would be any interest in Dembele.
The tweet translates as: "Barcelona are probing several clubs to see if they’d be interesting in taking Dembele."
Sapares did not mention Liverpool specifically but several media sources believe that the Reds would be among the clubs who might make a move for Dembele in the summer.
The Metro reports that the Reds' manager Jurgen Klopp has been a fan of Dembele ever since the Frenchman joined his former club Dortmund from Rennes in 2016.
However, Barcelona would be looking to cut their losses for Dembele and it is unlikely that Liverpool would be prepared to offer anything like the £97m that Barca forked out to sign the youngster last summer. A loan move might be more likely.
Another reason that Dembele has struggled for game time at the Nou Camp is because of the strength of competition around him. Philippe Coutinho has fitted in nicely as the third piece of the front line jigsaw alongside Lionel Messi and Luis Suarez.
Not that Dembele would find it any easier to break into Liverpool's front three of Mo Salah, Sadio Mane and Roberto Firmino, who have scored 90 goals between them this season.