Odemwingie looks set to leave The Hawthorns in the close season after a series of ill-advised Tweets and misdemeanours in the second half of the campaign.
The Nigerian was linked with a move to QPR in January but no deal was struck with the player bizarrely turning up at Rangers' training ground to complete the deal before the clubs had agreed a fee.
His value will have surely diminished due to his behaviour then and since but Clarke is insistent his £4million market value remains the same despite him having six months less remaining on his current deal now.
"He has signed a contract," said the Albion chief.
"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."
Clarke prefers to focus instead on Sunday's season finale against champions Manchester United - and he has urged his side to spoil Sir Alex Ferguson's retirement party.
Albion have already achieved their best Barclays Premier League finish and are aiming to break the 50-point barrier and finish in the top eight.
However, after a superb first half of the season, their form dipped drastically over the winter period and has slumped again in recent weeks with three consecutive defeats culminating in a 4-0 defeat by Norwich last weekend.
Clarke's men have the chance to end the season in style on Sunday by beating the champions in Ferguson's final match before retirement at the Hawthorns and the Scot is insistent they give a good showing.
"We're not there for a party on Sunday," warned Clarke, who will share a special bottle of red wine with his counterpart after the match.
"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."
Clarke admitted the heavy defeat by Norwich was hard to take and wants more from his men this weekend.
"I'm not hoping for a response, I know I will get one," he said.
"This is a group of players who know how to respond to adversity and know how to get results in the Premier League. That's why they are where they are in the table.
"Everybody is saying about the bad run we're on but you have to have a sense of perspective about what we're doing at this club, and that is achieving year-on-year improvement."