Liverpool great Gerrard is now an academy coach at Anfield and was priced at 8-11 by William Hill to take over at Rangers.
BetVictor had him at 4-7 while Skybet’s odds were 8-15 on Gerrard being Rangers manager for the first league game of next season.
King was seen at Anfield during BT Sport’s coverage of Liverpool’s 5-2 win celebrating close to Kenny Dalglish when Mo Salah scored his second goal.
Graeme Murty is in charge of the Ibrox club until the ends of the season but is not expected to land the job on a permanent basis.
Gerrard, 37, who made over 500 appearances for Liverpool in a storied career, was appointed youth coach at Anfield in February last year.
He has no management experience.