David Moyes has been searching for a new center-midfielder to compete with Declan Rice and Tomas Soucek since club legend Mark Noble announced his retirement.
Although Flynn Downes left Swansea City this summer for an estimated £14 million, the Hammers are willing to spend big on another of their top midfield targets.
Sky Sports News reports that West Ham and Lille have now come to terms on a deal for Onana to be signed this summer for a base price of €40 million (£33.5 million) plus add-ons.
According to the report, the Hammers had previously had three bids for the 6'5" midfielder rejected, but their fourth offer was accepted.
Onana's transfer to the London Stadium is not believed to be imminent, though, as West Ham and the player have not yet reached a personal agreement.
Onana, who Lille acquired from Hamburg for just €7 million (£6 million) last summer, is said to be difficult to part with, but the French club believes that there may not be a better offer in the future.
Onana began his professional career with German club Hoffenheim, but failed to make a single senior appearance before joining Hamburg in 2020.
The midfielder was unable to help Hamburg secure promotion back to the Bundesliga in the 2020-21 campaign, but his performances caught the eye of Ligue 1 champions Lille, who tied him down to a five-year contract last summer.
Onana made 41 appearances for Les Douges last season, including eight in the Champions League, although he was only named 15 times in the starting lineup.
Nevertheless, Onana’s impressed Belgium head coach Roberto Martinez, who handed the midfielder his international debut against the Netherlands in the UEFA Nations League in June.
Should Onana agree to personal terms with West Ham, he will become Moyes’s fifth signing of the summer window, after the arrivals of Downes, Nayef Aguerd, Alphonse Areola, and Gianluca Scamacca.
The Hammers also have their eyes on other transfer targets this summer, with Sky Sports News claiming that they are in talks with Burnley regarding a move for Maxwel Cornet.
The East Londoners are keen to take the 25-year-old winger on an initial loan deal with an obligation to buy next summer based on specific player and club performances.
Cornet, who is understood to have a £17.5m release clause following Burnley’s relegation to the Championship, missed the club’s opening league fixture against Huddersfield Town last Friday.
West Ham also remain in talks with Eintracht Frankfurt over a potential deal for versatile wideman Filip Kostic, although they have been told by the German outfit that they must increase their offer to £16.8m (€20m), having previously seen a bid worth £12.6m (€15m including add-ons) rejected.