The 33-year-old has been told that he does not feature in new manager Ronald Koeman's plans for next season and that he is free to leave the club during the current window.
Suarez has been heavily linked with a switch to Juventus, but remains in talks over cancelling his contract at Camp Nou with Juve unwilling to pay a transfer fee for the striker.
The Uruguay international has one year remaining on his contract in Catalonia and is pushing for that to be paid out in full if Barcelona want to offload him.
A clause in Suarez's contract would see him trigger a further 12-month extension if he plays 60% of games this season, and ESPN reports that he could therefore be frozen out next term if he does not leave during the current transfer window.
Barcelona would reportedly be willing to let Suarez leave for a nominal fee this summer, but are not prepared to pay off the final year of his contract.
The former Liverpool striker, who scored 21 goals last season, is understood to have already agreed personal terms with Juventus.