The Nigerian forward has publicly stated his desire to leave The Hawthorns, and faces disciplinary action over comments made on Twitter criticising Albion.
The club rejected Odemwingie's transfer request on Friday and continue to stand firm in the face of renewed interest from QPR.
Sporting director Richard Garlick said: "QPR have made a second, improved offer for Peter, which we have turned down.
"As we have repeatedly stated, we have no need or desire to sell our core players.
"Since we turned down Peter's transfer request, he has made his position clear in a statement to the media and via his personal Twitter account.
"This matter will be dealt with internally."
The Birmingham Mail reported that Odemwingie will be fined two weeks' wages - around £80,000 - for anti-Albion comments on Twitter at the weekend, despite issuing a partial climbdown on Sunday.
Odemwingie tweeted: "Looked through my tweets. Deleted some. Was too much. Only excuses - home alone, dark, son and wife in hospital, frustrated."
On Saturday, he tweeted: "I can understand the reaction of few Albion fans on my desire to leave the club. Real reason? Cos they once doubted my commitment.
"Want to know why I wanted to quit top flight football last summer earlier than I wished to? They know at the club.
"Albion fans are not the only reason, but made it easier for me to decide to stay and try my best to forget about the disappointment.
"I succeeded in doing that. But it's not getting better. Before bigger disappointment comes one day, I better leave on a good note.
"Best compliment I have ever received in my (career) as a player, manager like HR spending to bring me for mission 'impossible'."
The transfer window closes at 11pm on Thursday.