The Turkey international, who only signed for Barca last summer, is set to leave the Nou Camp after being told by manager Luis Enrique that he is surplus to requirements.
Arsenal were thought to be lining up a bid for Turan, having expressed an interest in him before he signed for Barca, but they have no need for another holding midfielder following the capture of Granit Xhaka.
According to Sport, Chelsea are planning to make contact with the Catalan club to see how much the 29-year-old will cost before deciding on whether to lodge a bid. However, it is understood that Barca will accept a fee of around £22million.
Fenerbahce and Galatasaray are also interested in bringing Turan back to his homeland but for the moment it appears that Chelsea are leading the chase to land him.