Cantwell is out of contract at Carrow Road in the summer but Norwich do have an option to extend his deal for another year.
And it would require a bid of around £15m-£20m for Norwich to consider selling the 23-year-old to their relegation rivals, according to Sky Sports.
Leeds United are also understood to be interested in the former England under-21 international, according to The Daily Mail.
Norwich currently sit bottom of the Premier League table, a point behind Newcastle in 19th.
The Magpies have already confirmed the signing of England international Kieran Trippier for £12million plus add-ons and are keen to bring in several more new faces in a bid to secure Premier League survival.