Odemwingie has apologised for his recent Twitter rants against the Baggies and for turning up without permission at Loftus Road on transfer deadline day, only for his move to QPR to collapse.
The Nigerian has been disciplined and fined by West Brom, and Clarke has urged him to reproduce the form he should in a "man of the match performance" in his last appearance for the club - a 2-2 home draw with Aston Villa three weeks ago.
Ahead of Monday's trip to Liverpool, Clarke said: "There are no winners in this issue. It was an episode in which there can be no winners. It is an unsavoury episode at the club and all I want to do now is move forward.
"Peter has paid a price and that's the way it should be. I know he has accepted the sanctions from the club, he's issued an apology and he wants to move on like we all want to.
"Our personal and professional relationship is fine. We had a chat in the summer, he stayed and made a good contribution to the first half of the season. Now he has to make a good contribution to the second half of the season.
"Is Odemwingie in the squad for Liverpool? That is still to be determined. It's something we have to look at over the next two or three days. I'll involve him when I feel it is right to involve him."
Clarke also ruled out the possibility of winger Jerome Thomas moving to Blackburn on loan, adding: "I've got a squad of 18 senior outfield players and three goalkeepers and that's my squad for the rest of the season.
"I can't let anybody else go. I can't bring anybody in or let anybody out."