Onyekuru made his debut for Eupen on September 5, 2015, in a 2-2 tie against K.F.C. Dessel Sport in the Belgian Second Division.
The 20-year-old scored 22 goals for the Belgian top-flight club last season and has been linked with various larger teams in Europe.
He helped the team get promoted to the Belgian First Division A in his debut season, and made his professional debut in a 3-0 loss on July 30, 2016, against S.V. Zulte Waregem.
However, the player is understood to have had a medical with Everton on Monday.
Onyekuru is expected to be loaned to Anderlecht for the next 12 months to continue his development in Belgium.
He is regarded by Everton director of football Steve Walsh and manager Ronald Koeman as one for the future