Former Brighton star Murphy has not featured for Rangers since suffering a serious knee ligament injury against Kilmarnock last August that ruled him out for the rest of the 2018-19 season.
The 30-year-old did return to action over the summer and featured regularly during pre-season, but he is yet to make a senior appearance since the campaign got underway and Gerrard suggested last month that he could be sent out on loan.
However, Murphy remained at Ibrox after the transfer window closed and Gerrard now appears to have done a U-turn by suggesting the Scotland international could feature over the coming weeks.
"He's showing signs that he's getting close", Gerrard told Rangers TV. "So, it wouldn't surprise me if you did see him in the coming weeks."
Gerrard admits that Murphy's chances have been boosted due to the injuries suffered by fellow wingers Jordan Jones and Ryan Kent.
"We might have to accelerate pushing him along because of the injuries to Jordan Jones and Ryan Kent, but I'm sure Murph is champing at the bit. He's waited a long time for a comeback game."
Indeed, Murphy could make his first appearance of the season when Rangers welcome Feyenoord to Ibrox in their opening match of this season's Europa League group stage on Thursday.