Barcelona want £26 million for the Turkish international which is what they paid for him last summer from Atletico Madrid.
Turan joined Barcelona on a five-year deal but had to sit out the first six-months on the sidelines before making his debut in January due to the FIFA transfer ban that was imposed on the club.
The Turkish international ended the season with a two goals and three assists in 810 minutes of La Liga football.
Turan was however, given just 46 minutes of playing time by head coach Luis Enrique in his last four league games.
Despite being linked with a move away from Barca, Enrique has always maintained that Turan will be at the club next season.
Arsenal and United were also closely linked with Turan last season but the Gunners may prove the more attractive destination considering he is looking for a house in London.
Turan also revealed last summer that he only wants to play for a side that plays Champions League football as it remains the last European trophy that he has yet to lift.