The Daily Mail says Odemwingie and West Brom team-mate Reid had a fierce bust-up after the Nigeria forward's aborted move to QPR.
Odemwingie was yesterday fined £75,000 by West Brom after his appearance at Loftus Road on deadline day.
And the striker, 31, confronted Reid in the treatment room at the club's training ground on Thursday.
Odemwingie was angered by comments attributed to Reid after last Sunday's defeat by Spurs in which it was suggested that he would not be made welcome.
But Reid stood his ground, insisting the striker would have to work hard to win over the rest of the team.