The Reds are looking at defensive options, after receiving the news that Joe Gomez was going to miss the start of the season with an achilles injury. The youngster missed the majority of last season, which he spent in the treatment room.
Mamadou Sakho also has an achilles injury, and is a doubt for the Reds’ league opener against Arsenal on August 14th.
And after selling Martin Skrtel, Jurgen Klopp is now considering bringing in a fresh defender, with the French centre-back one of his top targets.
Mathieu has made 49 league appearances for the La Liga champions across his two-season spell at the Camp Nou, scoring his first league goal against Real Madrid in a 2-1 victory in his first campaign.
However, the Reds may have to move quickly, with Le10SPort reporting that Besiktas have made an offer of nearly £6million for the French international.