Odemwingie released a series of outbursts against the Baggies after his transfer request was rejected last Friday.
The Nigerian international has expressed his desire to join QPR, who had a second bid - believed to be in the region of £3million - rejected by Albion.
The 31-year-old was given time off because his recently-born son, Noah, and wife, Sarah, have been in hospital but they were discharged on Monday.
Odemwingie is expected to meet with Albion officials to discuss his social networking remarks and he faces the possibility of a fine.
Baggies head coach Steve Clarke will have the chance to make public his thoughts on Odemwingie's attacks when he faces the media this afternoon ahead of Wednesday's trip to Everton.
Odemwingie has deleted some of his more inflammatory remarks from Twitter but it is understood the outbursts have not been looked on favourably by the Midlands club.
Even QPR boss Harry Redknapp intimated that Odemwingie's rants were ill-advised and had not helped in terms of trying to push a potential deal through.
Odemwingie has posted another Twitter message saying "Between now and the summer will show you all a money move! Busybodies!"
He followed that up by tweeting: "Didn't tweet that feeling down. But I am fed up. Son and wife back home from hospital. Glory be to God."
Albion have consistently stated that they have no desire or need to sell any players during January.