The 31-year-old has been targeted by the West London outfit since the start of the January window but the Baggies, who have already turned down an offer from the R's, have reiterated that they will not be selling any players this month.
West Brom's firm stance prompted Odemwingie to lodge a transfer request and took to Twitter to air his frustrations at the Premier League club.
Sporting and technical director Richard Garlick told the club's official website: "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."
Odemwingie has been with the Baggies since 2010.