The Istanbul giants are in the market for a new centre back following Bruno Alves’s red card in the Intercontinental Derby against rivals Galatasaray.
The Portuguese international has been removed from the squad and is expected to leave Fenerbahce in January.
29-year-old Agger moved to Brondby this summer but Fenerbahce are hoping the lure of Champions League football next season, could tempt the experienced defender to move to Istanbul in January.
Fenerbahce are reportedly ready to launch a loan bid for the Denmark international with the option to sign the player at the end of the season.
Agger spent eight years at Liverpool and left this season after a dispute with manager Brendan Rodgers.
“When you are a part of the starting eleven for several games in a row and the team have performed well, and you feel that you have played well, then you are left out of the team and don’t feel appreciated, it starts to get pray on your mind and you wonder.” Agger stated in an inverview with TV3 sport.
Agger has made seven appearances for Brondby this season.