The Liverpool legend won the Premiership title as Gers manager before being tempted to the Premier League by Aston Villa.
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Currently a free agent after leaving Al-Ettifaq of the Saudi Pro League, Gerrard is now being discussed inside Ibrox.
Gers want to find a new permanent manager after the dismissal of Philippe Clement. Caretaker manager Barry Ferguson will not be kept on, says talkSPORT.
Gerrard is a contender, as is fellow free agent and former Southampton manager Russell Martin.
Tottenham assistant coach Ryan Mason and former Luton boss Rob Edwards are also on the shortlist for the Gers board.