The Germany international winger is currently with Galatasaray in Turkey, but has not played for the last six months after they failed to register him in time during the August transfer window.
They will have to wait until the January transfer window to register him, but the player is reportedly set to give up and seek a move away as a result of the frustrating situation.
That has alerted his former manager Jurgen Klopp, who could be ready to make him one of his first signings at Anfield, according to the Mirror.
The 27-year-old can play in a number of positions in both defence and midfield, and would provide Klopp with both competition and cover in several areas.
He would be a particular boost in defence, with Klopp’s side having picked up a number of injuries in that area and finding themselves short on numbers, with several players out long term.
He only moved to Turkey for £1.5m, meaning he is unlikely to command a big fee, while his wages also fit within the current structure at Anfield, making a move a distinct possibility.