Coutinho joined Barcelona from the Reds in 2018 for a fee that could eventually rise to £142m, but the Catalan club want to get rid of him before that can happen.
According to Sport, Barcelona Coutinho off their books as soon as possible as if he reaches 100 games, a clause will be triggered to pay Liverpool £18m.
Coutinho has currently played 90 official matches for the club and was thought of by Ronald Koeman as a key man in his evolution of the team.
The Brazilian playmaker has featured 12 times in all competitions this season but also struggled with injury.
Barcelona are struggling financially, having been hit hard by the coronavirus pandemic and a massive squad wage bill, not bolstered by fans attending games.
Coutinho would have already reached 100 games for the team had he not been loaned out to Bayern Munich, who he helped win the Bundesliga, German Cup and Champions League last season.
The new club president will be elected by the end of January but by that time, Coutinho could have already played the 10 extra games needed to activate the expensive clause.