The £700,000-rated Welsh international midfielder is said to be interested in a move away from Ninian Park and has caught the eye of City boss Glenn Roeder.
Parry was signed by the Welsh side from Hereford for £75,000 in January 2004 and can play on the left wing or in a central attacking position.
This is the second midfielder to be linked with the Canaries in recent days, with Plymouth's David Norris also reportedly on Roeder's January shopping list.
