Hodgson wants Odemwingie talks
Odemwingie joined West Brom for £1 million from Russian side Lokomotiv Moscow in August 2010 and has scored 14 goals during his first season in the Premier League.
The Nigerian international's goals have helped secure the Baggies' top-flight status for another season and, after proving himself at the Hawthorns, he can expect an improvement on his current deal, which has one year left to run.
Hodgson said: "I'm pretty sure the club would be prepared to discuss an extension of Peter's contract. It would surprise me if they aren't. If that happens, it would be deserved.
"The chairman (Jeremy Peace) works here in a sensible way. He rewards success and he rewards people for doing a bit extra."
Hodgson's arrival at West Brom in February coincided with a lean spell for Odemwingie, who was dropped from the first-team. However, the 29-year-old fought his way back into the team and has impressed his new boss.
Hodgson said: "I left Peter out of a couple of the early games which I suppose was never going to endear him to me. He wasn't scoring at the time, people were beginning to doubt his ability and that was shining through a little bit in terms of his attitude throughout.
"That's what front players are like. They are moody people. When they are scoring goals, the world is a beautiful place.
"When they stop scoring goals, everything is wrong with the world and it is everyone's fault except their own. That's the way they operate as a breed."