However, Simpson is also being tracked by Queens Park Rangers and Fulham, and reports suggest he would like a move to London.
The full-back’s future at Newcastle United remains in doubt after talks over a new contract stalled, with Simpson wanting more than the £25,000-per week he is being offered.
Mike Ashley insists he will not raise it any higher, because Alan Pardew is hoping to sign a right-back this summer - suggesting Simpson will only be a squad player next season.
The defender has just a year left on his present deal, and has been urged by boss Alan Pardew to put pen to paper or move on.
Hughton signed him for United, and he would be happy to take him to Norwich.
Simpson is on holiday in the United States at the moment.