BBC Sport says Gerrard withdrew from the interview process on Saturday.
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The former Gers manager is keen to return to Ibrox for a second stint, but not at this stage in his career.
The Liverpool great met with Gers officials on Friday, with talks progressing positively. But Gerrard decided against pursuing the job on Saturday.
Gerrard led Rangers to the Premiership title in 2020/21.
His decision leaves Rangers still in need of appointing a new manager after the dismissal of Russell Martin last week.