The 21-year-old's loan deal was set to expire this month but the shot-stopper will now remain with the League One club until the end of the season.
Norman said: “It makes loads of sense for me to stay. I've enjoyed my time here so far and I'm happy here, so I'm glad the loan has been extended so early in the window.
“I've loved being at the club, and I'm grateful to have had the opportunity to make my EFL debut and to have played in the Checkatrade Trophy and the Carabao Cup.
“Steve [Collis] is a great coach and I get on really well with Josh [Lillis] and Brad [Wade], too, but within that, we're always pushing each other in training to become the best, so it's very competitive."