Rangers are seeking a new manager after the sacking of Russell Martin on Sunday.
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Gerrard, 45, is available after leaving Saudi Pro League club Al-Ettifaq in February.
The Guardian says a return to Ibrox could now be on for Gerrard, who left Rangers four years ago for Aston Villa.
With Gers, Gerrard broke Celtic's stranglehold on the Premiership title in 2020/21 - their first league triumph since 2010/11.