The 25-year-old's father and adviser, Keith Campbell, admits he would welcome a possible move to Hull, but that the Black Cats will have the final say.
"Fraizer is aware of what Steve Bruce has said about being interested in signing him and he would definitely be interested in coming back to Hull," Campbell snr told The Journal.
"He is very impressed with the way they play and feels he would fit. He is also a big fan of Steve Bruce.
"The problem is it is difficult at present, as there has not been any approach as of yet that Sunderland have told us about.
"Martin O'Neill has not given any indication as to what may be going on, and he will be the key to whatever happens this month.
"He hasn't been playing Fraizer as much as we would like, and he brought in Steven Fletcher, but he's not saying anything about letting him go either. We will have to see what happens."