Sources close to the Baggies have confirmed that Twitter statements by players form part of the club's disciplinary code of conduct.
Odemwingie again tweeted late on Sunday night: "Looked through my tweets. Deleted some. Was too much. Only excuses - home alone, dark, son and wife in hospital, frustrated."
But the 31-year-old faces the possibility of being fined two weeks' wages given the strength of his outbursts over the weekend.
Odemwingie has indicated his desire to join QPR during the current transfer window and had a transfer request rejected by West Brom on Friday.
Rangers had a £2million bid turned down at the start of the window but are expected to make another offer before it shuts at 11pm on Thursday.
Albion, who also rejected a £5m bid from QPR for defender Jonas Olsson, have constantly said no senior players are for sale this month.
But they have to weigh up whether Odemwingie's remarks have made his position untenable with both the club and supporters, who have been quick to hit out at his outbursts.
Odemwingie 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 spending to bring me for mission 'impossible'."
Then yesterday 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."
Albion have so far declined to make any public response to Odemwingie's comments, with head coach Steve Clarke due to face the media on Tuesday ahead of Wednesday's clash at Everton.