Liverpool boss Brendan Rodgers has insisted Mario Balotelli will not be going out on loan in the January transfer window.
The 23-year-old played 30 times for Barca's first team under Pep Guardiola during the 2011/12 season, but suffered a serious knee injury towards the end of that campaign that required surgery.
When he returned to action Cuenca joined Ajax on loan in January, 2013 ,but saw his spell in Holland cut short by another knee injury. Cuenca has been linked with a move to Primera Division newcomers Deportivo La Coruna.
A Barca statement read: "Barcelona told the player Isaac Cuenca that he is not part of the plans for the next first-team squad for technical reasons. The player, after a few days of consideration, has accepted the club's proposal and both parties have agreed to today rescind the contract that ran until June, 2015."