The 21-year-old has spent the last six months on loan with Coventry City in the Championship.
At the end of the season he will return to Old Trafford, where a fresh deal will be waiting for him.
"I have an offer for another year at Manchester United," said Norwood. "It's my big dream to play for United - but I want to have a successful career, wherever that is.
"Every footballer just wants to be able to play football."
Norwood is yet to make a senior appearance for the Red Devils.