Odemwingie made the comment on Tuesday during the latest in a string of Twitter outbursts directed against his employers.
On Sunday, the Nigerian used the social networking site to hit out at being a substitute in recent games, a move which followed his failed attempt to engineer a move to QPR in January.
The 31-year-old, West Brom's top scorer for the past two seasons, has 15 months remaining on his four-year deal but may seek to force the issue over his future when the squad reconvenes for training today following two days off.
Odemwingie, who joined West Brom in 2010, said of himself in a tweet posted on Tuesday: "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."
Article 17 of FIFA's transfer regulations states players over the age of 28 can end their contracts two years after signing for a club by paying a compensation figure arrived at by taking into account their wages and transfer fee.
Albion have already confirmed Odemwingie's recent outbursts will be dealt with internally.
Press Association Sport understands he is likely to face another fine, having received the same punishment over his antics during the January transfer window.
It is also understood the club will not sack the player, who was the subject of a £2million bid from QPR in January, as they still view him as a saleable asset.