The 22-year-old goalkeeper endured a frustrating time under Magilton, sitting on the substitutes' bench 101 times during the Irishman's reign.
Supple last featured for the club back in August 2008, but has decided to sign a new one-year deal under new boss Roy Keane and fight Richard Wright for the number one shirt.
"I played with Jim Magilton and worked for him for three years. I have a lot of time for him but it did not work out for me under his management and I would have taken my future into consideration if he had stayed in charge," Supple told the East Anglian Daily Times.
"Once the new manager offered me a chance to stay I talked it over with one or two people and made my decision to give it a go under his regime.
"A one-year deal suits me fine, and it goes without saying that this is going to be a massive year for me when I will be doing all I can to knock Richard Wright from the number one spot."