Philips has been linked with West Brom for a number of transfer windows, but they have still not got a deal over the line.
QPR wanted £10 million for the Scotland international back in January, but they have now dropped their asking price by 50%.
Rangers realise that they need to cut costs to adapt to Championship life, and Phillips is one of their top earners.
West Brom are keen to offer the former Blackpool man a chance to show his skills at the top level, and they now want to get the transfer over the line quickly.
Tony Pulis wants to sign Phillips before the end of the week, to ensure that he is with the rest of the team before they go on tour of Austria.
West Brom are due to fly to Austria next week, and Pulis wants Phillips to have the chance to spend the entirety of pre-season with his new teammates to give him the best chance to adapt to life at the Hawthorns before the competitive campaign starts.