The 18-year-old, whose current deal ends next summer, impressed during City's pre-season tour of Hong Kong and China.
He is currently gaining first-team experience at Watford during a loan spell which expires in January.
But Mutch, who was loaned out to Hereford and Doncaster last season, is keen to remain at St Andrew's on a long-term basis.
Mutch told the Birmingham Mail: "My contract finishes at the end of the season and we are talking to try and sort something out now.
"Hopefully that will be done as I'd love to re-sign. I don't plan to on going anywhere else.
"Then it is down to the manager whether he keeps me or not - or I go out on loan again to keep learning and improving."