Mills spent last season on loan at Middlesbrough and they were hoping for a permanent move before a public falling out, while Birmingham are also keen to bring him to the Midlands.
The 27-year-old Mills said: "I will look at every possibility and, if Norwich came in with an acceptable offer, I would be happy to play there."
The Norwich-born international played 73 times for his home-town club before joining Charlton Athletic.