Martin lasted just 17 games at the club and receiving his marching orders after a 1-1 draw at Falkirk on Sunday, much to the delight of supporters who witnessed him be given a police escort away from the stadium after many tried to stop the team bus from leaving.
The English coach left Rangers in eighth and 11 points adrift of leaders Hearts who are making a title charge against rivals Celtic this season. The Scottish side are now looking for a replacement and Defoe has thrown his name into the hat.
Speaking on talkSPORT, Defoe says he is ready to take over the club if he ever receives the call.
"I'll be straight on that flight or train. I think it's well documented how much I love that football club.
"The boy from the East End, (at the) back end of his career, goes to a club like Rangers. I was a massive Coisty (Ally McCoist) fan when I was a kid.
"I was privileged enough to play for the football club. I understood what it meant to play for the football club and the badge.
"If I had the chance, and I've said it many times, if I had the chance to go to that club in any sort of capacity, for me, it's a no-brainer."
Defoe spent three years at Rangers between 2019 and 2022, initially as a player and then in a coaching capacity. Although he lacks experience, many feel like he would do a much better job than Martin who is one of the worst managers in club history.