The 45-year-old had been seen as the front-runner to replace the sacked Russell Martin at the Scottish Premiership club.
But it is understood that after holding constructive discussions, the ex-England midfielder felt the timing was not right for a return to Ibrox.
Martin was sacked last weekend after just four months in charge, with the team having won just one of their opening seven Premiership matches.
Gerrard was previously in charge at Rangers between 2018 and 2021, winning the Scottish title in the 2020/21 season before leaving to take charge at Aston Villa.
He left his role in charge of Saudi Arabian side Al-Ettifaq in January.
Other names to have been touted as potential successors to Martin at Ibrox include Hearts boss Derek McInnes, former Rangers player Kevin Muscat and ex-Everton boss Sean Dyche.
AFP