Boro have already lodged a £6 million bid for the 24-year-old, but QPR have rejected the offer.
Rangers want £8 million for the skilful wide man, and Middlesbrough are not prepared to meet that asking price.
Boro rate Phillips, but they feel that he is being overvalued by QPR - and will now look towards other attacking targets to improve the quality of their squad.
QPR are under little pressure to sell Phillips, but they are apparently willing to cash in on the winger should their asking price be met.
Jimmy Floyd Hasselbaink’s side’s chances of promotion this season look slim, and the London club are, therefore, planning to reduce their expenditure on wages.
Phillips has scored five times and created three goals in 27 Championship appearances for QPR so far this season.