Hargreaves is available on a free transfer after his contract expired at Manchester United as has released videos on YouTube in an attempt to prove his fitness.
However, with Hargreaves having made only two brief appearances over the last two seasons, Hodgson has indicated that a deal is doubtful.
He told the Express & Star: "Owen has been in contact with [Albion technical director] Dan Ashworth and I think he wants to meet up with us, but we've got to be realistic.
"We're talking about a player who hasn't played for three years. He is a big name player but so is Bobby Charlton! I think one of the last games Hargreaves played was in my first season at Fulham which is over three years ago, so we've got to be realistic."