Gerrard turned down the chance to return, with the timing of the move believed to be behind his decision.
The former Liverpool and England captain held talks with the Scottish Premiership club last week following Russell Martin’s dismissal as head coach.
Those discussions were thought to have gone well but the 45-year-old opted against a second stint in Glasgow.
It leaves the fledgling Rangers hierarchy searching for a head coach to succeed Martin, who lasted just 17 matches after being appointed in June.
They sit eighth in the Scottish top flight, having won just once in their opening seven league matches, with their next game the visit of Dundee United next Saturday.
Martin was appointed on a three-year deal following a takeover of Rangers by a US-based consortium in the summer – led by now-chairman Andrew Cavanagh.
It took Rangers until late September to win in the league and they were humiliated 9-1 on aggregate by Club Brugge in the Champions League play-offs.
Martin left with the club 11 points behind leaders Heart of Midlothian and nine behind Celtic, having overseen five victories in all competitions.
