The Gers are assessing their goalkeeping options with number 1 Allan McGregor now 41 years old and backup Jon McLaughlin due to turn 36 years old later this year.
Gunn is not certain of being Norwich’s number 1 under David Wagner and Rangers are watching his situation at Carrow Road.
Rangers director of football Ross Wilson knows Gunn well from his time at Southampton and the shot-stopper could fit the bill for the Gers.
A move to Rangers would also let Gunn push himself into the thoughts of Scotland manager Steve Clarke.
Gunn is open to representing Scotland on the international stage.
The 27-year-old goalkeeper has made 14 appearances in the Championship for Norwich so far this season, keeping two clean sheets.
He is on a contract at Norwich which is due to run through until the summer of 2025.
