Odemwingie has not rested on his laurels after making a series of complaints via the social networking site on Sunday in which he hit out at being a substitute in recent games and seeing his commitment questioned in the wake of his attempts to engineer a January move to QPR.
Now the 31-year-old, who has been given a couple of days off with the rest of the senior players, may be set to force the issue regarding his future at the Hawthorns.
Odemwingie, the club's top scorer for the past two seasons, has 15 months remaining on his four-year deal.
But, under article 17 or FIFA transfer regulations, players over the age of 28 can end their contracts two years after signing for a club by paying a compensation figure determined by their wages and transfer fee.
Odemwingie tweeted: "I see a free player. A player who buys out his contract soon. Or a retired player. Does he look like he cares much? They made him not to."
His stance appears to indicate he is determined to bring the situation to a head after three months of verbal attacks against the club.
Albion have already confirmed the behaviour of the Nigeria international will be dealt with internally.
Press Association Sport understands Odemwingie is likely to face another fine after being hit in the pocket for his actions in January.
It is also understood the Baggies will not sack Odemwingie for whom they rejected a £2 million bid from QPR during the transfer window.
They still view Odemwingie as a saleable asset although which clubs would now take a chance on signing him remains to be seen.
Albion will not ban Odemwingie from using Twitter although any activity by players is governed by the club's disciplinary code of conduct.
Odemwingie's initial attack in January came after West Brom rejected his transfer request.
Then he turned up at Loftus Road on transfer deadline day without permission, only for his proposed move to QPR to break down.
Odemwingie even revisited that episode on Tuesday when he tweeted: "A simple phone call to return back would have been enough for me to return and deal only with laughs about saying bye to teammates.
"31st Jan. If there was a prise (price) in the afternoon, there should still be one in the evening. Simple."