City boss Stuart Pearce has accepted a bid for the 21-year-old, believed to be £800k, and he has now spoken to the Canaries about joining them before the start of the season.
"There are one or two clubs who have been interested in Lee, but Norwich are the ones who have come up with a fee we find acceptable," Pearce told the official City website.
"Lee has spoken to Norwich and now we are just waiting to hear whether he is going to leave or not."
Croft started 4 league matches last season, scoring on his full league debut at Fulham in November. He also made 17 substitute appearances and spent a loan spell at Oldham the previous season.