The 19-year-old has not made a first-team appearance for Town and is currently on loan at League Two strugglers Stockport.
Jewell has also confirmed that youth-team players Rory McKeown and Josh Meekings will not be offered a deal and will also leave the club.
Jewell said: "It's the worst part of a manager's job, telling young players you won't be keeping them on.
"But the challenge for those boys now is to go on and have a career in the game elsewhere.
"We will do everything we can to help them achieve that and we wish them all the best."