The Ibrox side previously had an initial bid of £3.8million turned down by Partizan Belgrade, but it is now being claimed an agreement has finally been reached.
Serbian outlet Mozzart Sport reports that a fee of €5.5m (£4.66m) has been agreed upon by the sides, with a 10 per cent sell-on clause added in.
The midfielder, 20, now looks set to head to Glasgow for a medical and to complete his move to Derek McInnes’ side.
Partizan’s new sporting director, Radosav Petrovic, had hinted that something was in the works for Dragojevic.
He said: “There are certain indications and I believe that in the coming days we will have more concrete information. It is an offer for Vanja Dragojević, and we have something for (Ognjen) Ugresic as well.”
