The Hammers have been pursuing new attacking options this summer and were keen to bring in the 20-year-old striker from KAS Eupen after he netted 22 league goals. In addition, he showed composure in the opposition penalty box and was good in one-on-one situations.
Celtic wanted to sign Onyekuru in the January transfer window and slapped in a bid of €1m for the 20-year-old, but it was rejected.
However, the player is understood to have had a medical with Everton on Monday.
Onyekuru made his senior debut for Nigeria in the 3-0 friendly win over Togo earlier this month.
Onyekuru is expected to spend next season on loan at Anderlecht as he does not yet qualify for a work permit in the UK.
Spanish under-21 striker Sandro Ramirez of Malaga has also been linked with the Merseyside club.
Everton have not yet announced the deal formally but the picture above suggests this could be imminent.
Ronald Koeman is still after his prime summer target Gylfi Sigurdsson and Burnley defender Michael Keane.
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