The 23-year-old centre forward is wanted by a host of teams, including Newcastle, Wolves and Marseille.
Amoura has been impressing in the Belgian league, with L'Equipe stating that a move to a bigger team is very much on the cards.
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The Hammers are said to have put in a 13 million offer to secure Amoura as soon as possible.
Incoming manager Julen Lopetegui has made signing forwards a priority for the club.
The Hammers have struggled on the goal front under manager David Moyes this term.