Kilmarnock manager Steve Clarke is also said to be under consideration by the Ibrox board after doing a stunning job at Rugby Park this season.
He has taken Killie from bottom of the Scottish Premiership to the top-six thanks to the sensational form of players like Kris Boyd, Youssouf Mulumbu and Jordan Jones.
Clarke has also had spells at West Brom and Reading.
During his time at The Hawthorns, he guided the Baggies to their highest-ever Premier League finish in his only full season when they ended up eighth in 2013.
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