The Nigerian striker, who attempted to leave The Hawthorns for QPR in January, again took to Twitter to criticise Albion over a lack of game time.
Clarke says the club will make a decision on the punishment they dish out to Odemwingie whilst making it clear that he has absolutely no time for his type of behaviour.
"I haven't got anything to say to him. If he's got something to say to me he should come and say it to my face," Clarke told reporters.
"He has to come to me. He's the one that has the grievance, not me. I am absolutely bored with the whole episode.
"I'm not interested in what he said. The club will deal with it.
"I don't read Twitter. I understand there were some more comments and I told [technical director] Richard [Garlick] and the club to deal with it in the way they see fit. Richard has been off ill. He hasn't been in.
"I'm just disappointed that I have to spend so much time talking about one player when I have such a fantastic squad of players who have made such a fantastic contribution this season.
"I am fed up of talking about one player."