The Albion boss pointed to the players very poor fitness record and says that this really should make such a move unlikely, although talks have been held between the two parties.
Free agent Hargreaves is desperate to find a club after getting his fitness back since being released my United, but Hodgson doubts very much that he will be moving to the Hawthorns.
He told the Express and Star: “Owen has been in contact with 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.”