Gunnarsson has found himself down the pecking order at the Madejski Stadium this season following the arrival of Brendan Rodgers as manager.
The Iceland international has made only 10 appearances in all competitions this term and is thought to be ready to move in search of regular first-team action.
Gunnarsson's agent, Olafur Gardarsson, admits a number of clubs are tracking the player's situation and that the versatile midfielder could move on next month.
Read more.. Sky Sports