The Daily Mail reports the 28-year-old is someone the Canaries think can help them in the Championship next season.
The relegated side want to bounce straight back up. They have already signed nine new players, and Hugill could be the tenth.
He has only played three sub games for the Hammers, and went to the Championship on loan at Middlesbrough and QPR.
Now he can leave for a decent fee, and it appears Norwich will pounce on the chance to sign him.