The 20-year-old defensive midfielder is a player West Ham have identified as a top target and they are keen to take him to the London Stadium.
He is considered to be a big talent at Lille and the Hammers have been pushing to secure a deal to sign him.
Lille rejected a €23m bid towards the start of this month from the Hammers and knocked back another €30m offer earlier this week.
But it has been claimed that West Ham remain interested in Onana despite the setbacks this summer.
The Hammers are in discussions within the club over whether to table another offer for the midfielder.
He has been extensively scouted and David Moyes is keen to add Onana to his squad.
Lille do not want to sell him but the financial reality of French football means they may not be able to resist another big offer.
Onana would be keen on a move to the Premier League if the two clubs reach an agreement over a fee.
