The 24-year-old arrived at Ibrox from Swindon Town earlier this month and is keen to show the England manager what he missed out on during his time as manager of Fulham.
Speaking in an interview with the Daily Record, Foderingham revealed it was Hodgson who had let him go as a youngster, while in charge at Craven Cottage.
“He had Mark Schwarzer and the Swiss international Pascal Zuberbuhler in front of me. David Stockdale was also in the queue,” Foderingham said.
“Roy just told me I had no chance. I would just have been training there and not playing.”
Despite this setback, the new Rangers recruit believes Hodgson's decision was actually to his benefit, with Foderingham earning his stripes during a series of spells in the lower leagues of English football.
Having moved from Fulham to Crystal Palace, the 24-year-old then spent time on loan at Bromley, Boreham Wood, Histon and Swindon before completing a permanent switch to the County Ground.
And with that experience under his belt, Foderingham believes he could yet stake his claim for a place in Hodgson's England squad.
The former Fulham trainee represented England at under-18 level alongside the likes of Jack Wilshere and is using the example of another former Glasgow-based goalkeeper as encouragement.
“Fraser Forster had some fantastic seasons up here with Celtic and rightly got into the England squad,” he said.
“So I can never give up on England. I’ve got to aspire to be the best I can be – and that’s the very top level.”
His first mission will be to dislodge Cammy Bell as Rangers first-choice keeper, with the pair likely to provide stiff competition for one another at the Ibrox club.