Per the source, the Black Eagles have have held talks with the La Liga champions but want to negotiate a lower price for the experienced French defender.
The report states that Liverpool boss Jurgen Klopp has the experienced defender on his radar as a potential solution to his current crisis at the back.
The Reds decided not to renew Kolo Toure’s contract and Martin Skrtel joined Fenerbahce last week. Meanwhile Joe Gomez is injured making Lovren and Matip the only two available centre-backs.
The report also claims that Barca asked Besiktas for €7 million in order to transfer the defender – a fee the Black Eagles are keen to lower.
Barcelona have already added strength to their defence over the summer bringing in Samuel Umtiti and Lucas Digne which has pushed Mathieu further down the pecking order.
Besiktas would be able to offer Mathieu the guarantee of first-team and Champions League football next season but Barca would have to accept a lower transfer fee than their current valuation if he were to make the move.