Albion turned down an initial bid at the start of the January transfer window, and they also refused Odemwingie's formal transfer request last Friday.
The 31-year-old has made no secret of his desire to join Harry Redknapp at Loftus Road despite QPR's perilous position, but the Baggies continue to insist he is going nowhere.
West Brom's sporting and technical director (designate) Richard Garlick said in a statement: "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," added Garlick, who also revealed that Odemwingie faces disciplinary action for a string of attacks on the club via his Twitter account.
The Nigerian repeatedly hit out at the Baggies for their refusal to grant him a transfer to QPR, although he has since deleted the offending tweets before apologising for the outburst.
He wrote: "Looked through my tweets. Deleted some. Was too much. Only excuses - home alone, dark, son and wife in hospital, frustrated."
But Garlick said: "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."
Redknapp later agreed that Odemwingie's tactics to force a move had left West Brom in a "difficult situation" but denied QPR were to blame for his behaviour.
He said: "It's not worked out in an ideal way, really, it's a bit too public. I'm sure West Brom are not too happy with the way it's gone, but it's not been our doing. We made an enquiry and the enquiry's leaked out."
Odemwingie had tweeted on Saturday: "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 (QPR manager Harry Redknapp) spending to bring me for mission 'impossible'."
And on Sunday he tweeted: "Offer came (from QPR), everybody knows. I ask club what they think ? Answer - not now. Maybe summer. I ask - or is it tactics to get more money?
"Answer- we have enough now there is no prise (price) for you. We need you.
"I say ok. What's the prise for summer? We will tell you after the window closes.
"I say - I have served the club well and deserve at least to have a prise now so I can plan my probably last move in England.
"Don't want another summer window not knowing what will happen cos now Ill have to move my little son elsewhere.
"After all I have contributed to the clubs success last two seasons I hoped to at least get a low prise. Answer - talk later.
"Last season January window is when I should have handed in transfer request. Was one foot in Rubin Kazan - not for sale. Fulham. Not for sale. Newcastle. Not for sale. Wigan. Not for sale.
"Loyalty left 70 percent. the rest they stole out of my pocket thinking I was keeping money in there."
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