Martin, 27, joined Norwich from Peterborough in January 2010 following a successful loan spell and was an integral part of the side which secured promotion to the top flight under former manager Paul Lambert and went on to retain their status for a third campaign following Hughton's appointment last summer.
Earlier this week, Norwich sold former club captain Grant Holt to Wigan and are anticipated to further bolster the squad ahead of a three-match tour to the United States.
The Canaries have already shattered the club's transfer record with the £8.5million capture of Holland international Ricky van Wolfswinkel.
Norwich are understood to be tracking PSV Eindhoven's Sweden international Ola Toivonen, Lokomotiv Moscow's £6million-rated Senegal striker Dame N'Doye and Blackburn left-back Martin Olsson.
Feyenoord midfielder Leroy Fer and Ajax defender Toby Alderweireld are also reported targets for the Canaries, with suggestions the duo have already travelled to East Anglia to take in the club's facilities ahead of undergoing medicals.
- Sports & Recreation
- Paul Lambert