The former Birmingham City and Aston Villa midfielder has reportedly struggled to adapt to life in the North East of England and is seeking a move back to the Midlands.
Wolverhampton Wanderers and Villa are reportedly interested in signing the 25-year-old, but it now appears that they face competition for his signature from the Baggies.
"He is a very good player, so obviously someone like Craig Gardner becoming available will alert the Midlands clubs or clubs in the near vicinity," Hodgson told The Mirror.
"But it will be a question of price and if there are clubs who think they can afford him.
"I don't think clubs will say, 'he is no good, we don't want him'."
Gardner has scored two goals in his time with the Black Cats.