The 31-year-old Nigeria international has made 17 appearances for Steve Clarke's side so far this season, scoring four times, and has also attracted interest from Newcastle United.
QPR manager Harry Redknapp is looking to strengthen his squad during this month's transfer window and hopes Odemwingie can bolster his attacking options.
With Andrew Johnson and Bobby Zamora both out injured, Redknapp has depended heavily on Djibril Cisse since taking over as manager in November.
Odemwingie has scored 30 goals in 81 appearances for West Brom following his £2million move from Lokomotiv Moscow two-and-a-half years ago.
However, he has had to share striking responsibilities this season with Shane Long, Marc-Antoine Fortune and the on-loan Romelu Lukaku.
Should he leave, Odemwingie is expected to cost in the region of £3million.
Newcastle registered their interest after it became apparent Demba Ba would be leaving Tyneside to join Chelsea.