The latest rejected bid came from Harry Redknapp and QPR, who offered £2 million for the Nigerian's services, but were told he was not for sale. That has outraged Odemwingie, who feels the club have not kept him informed of their plans for him in the future.
"Offer came, everybody knows", he told the Daily Mail.
"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," he continued.
"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 I ll 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."
These events have left Odemwingie bemused at the Hawthorns, and the striker feels let down by West Brom - the club he believes he has served well in the last two seasons.
"Loyalty left 70 percent. the rest they stole out of my pocket thinking I was keeping money in there," he said.
"I can understand the reaction of few Albion fans on my desire to leave the club. Real reason? Cos they once doubted my commitment.
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Odemwingie has been blasted by the Baggies' faithful for his stance, with earlier Twitter comments by the striker also causing dismay, but he insists it was the fans who persuaded him to stay in the past.
"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."
QPR are expected to make an improved bid before the January transfer window closes on Thursday, and after Odemwingie's comments, it remains to be seen whether he will soon be shown the exit door by the Baggies.