He has been installed as second favourite by bookmakers behind another former Rangers star Giovanni van Bronckhorst.
Martin, who played 29 times for Scotland, spent a short spell at Ibrox in the second half of the 2017/18 season, playing 17 times for the club.
The 35-year-old has developed a strong reputation in English football thanks to his work with MK Dons, turning the side into a possession-based team.
Former Scotland youth international Zak Jules explained what it was like to play under Martin.
"The way we play, we almost demoralise teams,” he said.
“We keep the ball so much that when teams do get the chance to keep possession – they’ve got no legs and, within no time, we’ve got the ball back and they don’t see the ball again for a while."
His job with the League One club earned him a move to Swansea City in the summer.
The Welsh side are currently 12th in the Championship.
However, according to the Glasgow Times, Martin is not in the running to be next Rangers manager.
It is reported he doesn’t feature on the club’s shortlist of potential successors.
Favourite Van Bronckhorst has title-winning experience with Feyenoord as manager and will understand the demands at Ibrox having won two league titles as a player.