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.