The Baggies attempted to bring the former Blackpool man to the club in the summer.
Tony Pulis' side were interested in a potential move for the 24-year-old during the summer, but could have more luck this time around with The Sun claiming that Hoops owner Tony Fernandes is ready to sell the Scotland international.
With just 18 months left on his current deal at Loftus Road, and with promotion back to the top flight looking very unlikely this season - with Rangers currently sitting 17th in the Championship - Fernandes is concerned that keeping hold of Phillips for any longer will seriously harm his value (via The Sun).
However, the Baggies will have to see off competition from the Cherries, who have certainly not been afraid to spend some money during this window. The arrivals of Benik Afobe and Lewis Grabban have seen the south coast club part with £19m already (via The Sun).
Despite Rangers' disappointing position in the table, Phillips has been in good form this term. He has four goals and three assists for Jimmy Floyd Hasselbaink's side, and also showed last season that he has what it takes to do well in the top flight.