Odemwingie, who famously turned up to sign for QPR on transfer deadline day in January only for a deal to fall through, looks certain to leave the Hawthorns this summer.
The Nigerian has repeatedly hit out at Albion over his treatment during the second half of the season, but Clarke is not willing to budge on a likely £4m price tag.
"He has signed a contract," said Clarke. "I think his goal record for West Brom is something like one in three.
"Whoever wants him has to pay the market value. Is that the same as it was in January? Yes. We are not a charity."
Meanwhile, Clarke is hoping to spoil Sir Alex Ferguson's retirement party when Albion take on Manchester United in Sunday's season finale.
A win could see West Brom finish in the top eight, and Clarke added: "We're not there for a party on Sunday.
"Our party will be with our supporters at the end of the game when the players get the chance to thank the fans and the fans get the chance to thank the supporters for the season.
"That's the only party we're interested in and we'll do what we can to finish on a high. We started the season on a high by beating Liverpool and we want to finish on a high against the champions.
"I'd be surprised if Sir Alex was just there to celebrate his last match as a manager. It's about competition and that's what he'll be there for."