The Daily Star says Reina, 30, is under contract at Anfield until 2016 but Liverpool are understood to be willing to listen to offers.
And Barca believe £8m will be enough to get him.
Reds boss Brendan Rodgers has doubts about Reina’s ability to distribute the ball in the former Swansea boss’ pass-first system.
With Victor Valdes ready to leave Barca, Nou Camp boss Tito Vilanova said recently: “We do not want to risk a young player in this position. We need a man with experience.”