Garner's injury could prompt Rangers manager Mark Warburton to add to his Ibrox ranks in January.
The 27-year-old Czech striker has only made two substitute appearances for the club this season and is entering the final six months of his contract.
The Turkish side have been linked with Aston Villa players before.
Libor Kozak has made 22 appearances for Aston Villa.
The Czech striker still loves his former club Lazio.
The Czech striker suffered a broken leg not long after initially signing for Aston Villa.
The Czech striker has only made two substitute appearances this season and has not featured for the first-team since Bruce's appointment in October.
Rushian Hepburn-Murphy's first-half strike failed to prevent Kevin MacDonald's side from falling to a 2-1 defeat at Villa Park on Monday night.
The Czech international striker can't buy a game at Aston Villa.
Striker showed a glimpse of his talent for Villa's under-23s.