He was the front-runner to replace Russell Martin, who was sacked after just four months in charge; Gerrard felt the timing was not right for a return to Ibrox, despite positive discussions with the club.
The former Rangers boss led the club to the 2020-21 Premiership title, their only league win since 2012.
Rangers Under-19 coach Steven Smith is currently overseeing first-team training, with other potential successors being considered.
Hearts boss Derek McInnes, former Rangers player Kevin Muscat and ex-Everton boss Sean Dyche are among the names linked with the vacant position.