Despite having already signed Chris Wood from Burnley earlier in the January transfer window, the Magpies have remained in the market for a second frontman.
Ekitike, who has contributed eight goals and two assists in Ligue 1 this season, was identified as a target several weeks ago, and it now appears that Newcastle have made a breakthrough in negotiations.
According to Sky Sports News, Reims have accepted Newcastle's latest offer for the 19-year-old, said to be between £20m and £25m.
The North-East outfit are also attempting to get a deal for Brighton & Hove Albion defender Dan Burn over the line, while interest remains in Manchester United midfielder Jesse Lingard. body check tags ::