Forest, whose boss Colin Calderwood has bolstered his forward line with big-name signings Andrew Cole and Robert Earnshaw already this summer and is said to be after Preston's Brett Ormerod, spurned overtures from Norwich earlier in the summer.
The Canaries have already taken midfielder Sammy Clingan from the City Ground and are desperate to beef up their forward line, which at the moment comprises only Jamie Cureton with any meaningful first team experience.
Tyson, 26, has turned down an extension to his contract and told the Evening Post, "They have said that I have to prove myself and I will - then get a better offer. As far as I am concerned, I have a year left on my contract which means we have a whole year left to talk about it."
The former Wycombe striker is unlikely to want to face another season on the sidelines, however, and could be tempted by guaranteed first team football at a rival Championship club.