Suarez has been told by new Barca coach Ronald Koeman that he is not part of the Dutchman's plans and has not featured in any of the club's three pre-season friendlies.
According to RAC 1, he has now reached an agreement to rescind his contract with the Catalan club and is now expected to leave in the next few days.
Meanwhile, Atletico have moved ahead of Juventus in the race to sign the 33-year-old, with El Mundo Deportivo claiming that the striker has reached an agreement with the Rojiblancos.
Suarez had looked set to join Juventus and travelled to Italy last week for an Italian language exam, part of the requirements for him to obtain an Italian passport.
However, Juve coach Andrea Pirlo was pessimistic about a possible deal on Sunday.
"It's very difficult for Suarez to arrive," he said. "Especially because of how long the passport will take.
"I know it will take a long time, so I think it's difficult that he can be our centre-forward."
In order to sign Suarez, Atletico need to remove one or two high-earning players from their wage bill.
The Rojiblancos are trying to find a new club for striker Diego Costa, while Alvaro Morata has been linked with a loan move to Juventus.