Everton could sell Onana this summer as boss Sean Dyche looks to raise funds for reinforcements and the midfielder would not be short of options.
Hammers boss David Moyes is an admirer of the Belgian and tried to beat Everton to his signature last summer.
He did not succeed, but is again on the hunt for Onana this summer.
However, it is unclear if the midfielder is open to joining West Ham and the London side face a wait to find out.
It is suggested that Onana would prefer to join a club playing in the Champions League if he ends his association with Everton.
That may mean a move abroad for Onana, unless Manchester City, Arsenal, Newcastle United or Manchester United come calling.
The 21-year-old midfielder turned out in 33 of Everton’s 38 Premier League games over the course of last season and was booked on nine occasions; he played the full 90 minutes in both of Everton’s meetings with West Ham.