The report claims that the La Liga champions are considering their options regarding the 29-year-old winger.
Turan joined on a £26 million move from Atletico Madrid over the summer but missed the first-six months of the season due to the FIFA transfer ban imposed on the club.
The bearded winger did end up making 25 appearances scoring twice and providing four assists but struggled for playing time towards the end of the season and managed just 46 minutes of playing time.
Turan made just nine starts for Barcelona but he still managed to achieve the highest pass accuracy in the team at 92 percent.
The Barcelona midfielder is capable of playing in central midfield, attacking midfield and on the wing. Turan has won every domestic title in Spain and every European trophy except the Champions League.
Turan has been selected for the Turkish national team squad for Euro 2016 but will not play against England tomorrow due to Barcelona playing in the Spanish Cup final against Sevilla.