The ex-Millwall hitman has endured a tough time this season, starting only two Premier League games under new Canaries boss Chris Hughton and finding the back of the net only once.
Hughton has showed a preference for a lone striker in Grant Holt with Wes Hoolahan working in the space behind and City's last four results have been good enough to lift them out of the drop zone and into the Capital One Cup quarter-finals.
Morison, 29, signed a three-year deal at Carrow Road when he arrived in June 2011 and City will be anxious to recoup as much of their £2million outlay as they can with his contract set to enter its last 18 months in January.
So far there has been little interest, but there are moves afoot to get Morison's name circulated around some ambitious Championship-level clubs willing to invest in a proven striker.
Morison scored 15 goals in the Championship two seasons ago and could be of interest to the likes of Leeds United and Nottingham Forest.