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.
Clarke made his intentions to keep hold of Odemwingie known at Tuesday's press conference, claiming he feels the player has been "really badly advised" by his representatives.
Clarke has cast doubts over whether Rangers will make an acceptable off before the transfer window closes on Thursday, but accepts Odemwingie will have to build bridges with fans, players and the club.
Odemwingie, who has made 13 Barclays Premier League starts this season, was due to meet with Albion officials to discuss his social networking remarks and he faces the possibility of a fine.
He has deleted some of his more inflammatory remarks from Twitter but it is understood the outbursts have not been looked on favourably by the midlands club.
Even QPR boss Harry Redknapp intimated that Odemwingie's rants were ill-advised and had not helped in terms of trying to push a potential deal through.