Odemwingie's future at the Hawthorns has been the subject of conjecture since he failed to secure a move to Queens Park Rangers in January.
The Nigerian international claimed last week that he was almost certain to leave the club this summer after coming in for criticism from Baggies fans.
Clarke has now conceded that Odemwingie, who came off the bench in Sunday's defeat to Norwich, will move on at the end of the season.
The Baggies boss admitted for the first time publicly that he does not expect the 31-year-old to be part of his squad next season.
"His future will be decided in the summer," said Clarke.
"Do I think he will be a West Brom player next season? No, I don't.
"I don't do the deals, I'm the head coach, but I was asked a question and I gave an honest answer.
"I don't think he will be here next season."