Vlaar is free to talk directly to other clubs with his contract set to run out at the end of the season.
The Lions have made strengthening their defence a priority in the summer however, there is uncertainty over who will become club president and manager.
Galatasaray star Wesley Sneijder is reported to have advised his fellow compatriot to consider moving to Turkey.
The Lions would be able to sign Vlaar in the summer despite exceeding the current foreign player ruling as starting from next season Süper Lig clubs will be able to sign 14 non-Turkish players.
Süper Lig clubs are currently only permitted to play five foreign players at any one time however, that number will be increased to 11 next season.
Several Premier League clubs are also reported to be keeping close tabs on Vlaar.