Turan joined the club from Atletico Madrid for 34 million euros ($41.46 million) plus add ons in July 2015, winning six trophies but only making 55 appearances and scoring 15 goals.
Spanish newspaper Sport last week estimated it cost Barca one million euros for each appearance made by Turan, taking into account an annual salary reported to be 8 million euros a year.
"During this period Barca reserve the right to transfer the player to a club belonging to UEFA, and will receive a variable fee according to his performances," said the Barca statement.
"Meanwhile, Istanbul Basaksehir will reserve the right to buy the player from Barcelona."
Turan quit the Turkey national team in June 2017.
($1 = 0.8201 euros)
(Reporting by Richard Martin; Editing by Ken Ferris)
