The Gers are now considering their options after parting company with Michael Beale and they have vowed not to rush the process.
A host of managers are being linked with the job at Ibrox, including current Kilmarnock boss McInnes.
McInnes has been a contender for the Rangers job before, having rejected an approach in 2017, and the Ibrox club will talk about him as a possibility as they weigh up their options.
Whether the 52-year-old, who played for Rangers as a player, will emerge as a favoured candidate remains to be seen.
McInnes though would bring instant Scottish Premiership experience to the job and has the benefit of knowing Rangers.
The Scottish giants have been linked with a host of potential candidates, including former Chelsea and Everton boss Frank Lampard.
Kevin Muscat, of Japanese side Yokohama, is another possible contender, along with AZ Alkmaar coach Pascal Jansen.
Steven Davis is currently in temporary charge of Rangers.