Gers sacked Philippe Clement on Sunday and Gerrard was immediately installed as among the favourites for the job.
Gerrard led Gers to the Scottish Premiership title before leaving for Aston Villa.
The Liverpool legend struggled at Villa and in Saudi Arabia withe Al-Ettifaq, where he left the post earlier this month.
However, given his success at Ibrox, there is a movement to bring back Gerrard.
Gers legend Ally McCoist recently stated: "It wouldn't surprise me if Steven Gerrard came back to Ibrox.
"He's obviously held in really high regard by the supporters because of the league title he won, and his next job is going to be vitally important for him.
"Things haven't gone according to plan for him after he left Rangers. A little bit like Frank Lampard going to Coventry – his next appointment was really important to him as well."