The former Birmingham player has reportedly been suffering from homesickness after moving to the North East last summer and there have been suggestions Wolves are considering a bid for him.
Sunderland manager Martin O'Neill said earlier this week he hoped Gardner, who was signed by Steve Bruce, would stay given his recent form for the resurgent Black Cats.
But transfer talk is gathering momentum and Hodgson is considering the 25-year-old as a possible solution to his injury-ravaged squad.
The West Brom boss said in the Daily Mirror: "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.
"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'."