Norwich manager Nigel Worthington told his club's website: "Jim Brennan is one of a number of players we've been looking at in recent weeks."
It is also thought relegated West Bromich Albion are keen to bring him to the Hawthornes on a free transfer.
Meanwhile Forest manager Paul Hart has announced that he is interested in aquiring the services of Israeli international striker Avi Nimni.
The 31-year-old plays for Maccabi Tel Aviv and has played 65 times for his country and scored 14 goals.
Paul Hart has a high regard for the forward. He said: "I think Nimni is an excellent player with great technical abilities. This is why I want him so much because he can add a lot as a footballer and as a leader."