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.
England Under-21 winger Nathan Redmond was last week purchased from Birmingham, while defender Javier Garrido has signed permanently after a loan from Lazio.
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.
Norwich, though, remain adamant England goalkeeper John Ruddy will not be sold, despite Chelsea having twice made formal offers. Indeed, the interest of the Stamford Bridge side could now fade following the signature of veteran Mark Schwarzer, who was a free agent after leaving Fulham.