Albion have rejected two offers from QPR for the Nigerian, the latest believed to £3million.
Odemwingie has handed in a transfer request and over the weekend hit out at the Baggies on Twitter, accusing them of "stealing" his loyalty and showing him a lack of respect.
Odemwingie launched a series of Twitter tirades against Albion after they rejected his transfer request on Friday.
He has not been included in the squad for Wednesday's game at Everton but Clarke insists that is not a disciplinary measure.
The player was given a further day off because his recently born son and wife have been in hospital.
Clarke said: "What has happened has been unfortunate, a situation that did not have to develop.
"QPR have put two bids in for Peter, the club have turned them down and feel at this time in this window the bids are not acceptable to us.
"The ball is back in QPR's court. They have to decide if they want to make another bid.
"Peter's comments haven't helped the situation but I feel he has been really badly advised.
"Harry Redknapp alluded to that yesterday when he was talking about gang warfare with agents fighting to get a bit of the deal.
"There have been a number of things going on behind the scene which have turned Peter's head a little bit and that is unfortunate for us, for QPR and Peter.
"Now we have got a situation that has developed over the last few days which is not good for anyone."
Clarke added: "Can we keep Odemwingie? Yes, I think we can because if QPR don't come up with a bid which is acceptable to West Brom, then I don't see what the solution is.
"You can't just let a player go. The club are entitled to get a good price for Peter in this window.
"If it doesn't happen and he is here on February 1, then it becomes a different story and there are different bridges to be mended and different conversations to be had.
"But like I say, the ball is in QPR's court. I personally hope he is here on February 1 and we can look forward to have him as part of our squad for the rest of the season."
Odemwingie will not be under consideration for the visit to Goodison Park.
Clarke said: "It isn't a disciplinary measure. Peter hasn't been in. His newborn son has been back in hospital, he came home yesterday [Monday] and we have given Peter another day off to make sure all is well."
As regards any possible action against Odemwingie, Clarke would only say: "It is not my department. The club will deal with that as they see fit and it will be dealt with internally and in private."