The Hammers have already roped on Flynn Downes from Championship side Swansea City to bolster their midfield but boss David Moyes is still keen on more signings.
West Ham have identified Lille man Onana as one of their top midfield targets and have already made three offers for him with the latest being around €38m.
The Londoners are yet to get a deal over the line for the Belgian but they have not give up on their hopes of signing him.
West Ham remain in talks with Lille over a deal for the Belgian and are pushing to snare him away to England.
The Irons and Les Dogues are discussing a fee for Onana and how payments could be structured to reach an agreement.
Onana only joined Lille last summer from German club Hamburg, but could find himself on the move following a single season in France.
Napoli man Piotr Zielinski another midfielder West Ham are trying to sign this summer, while they remain keen on Eintracht Frankfurt’s Filip Kostic.