The Hammers are selling talisman Declan Rice to Arsenal and boss David Moyes is keen to make sure he is adequately replaced in midfield.
Moyes is an admirer of Onana and tried to beat Everton to his signature last summer, but the midfielder preferred to head for Goodison Park.
Everton could sell Onana this summer though as they look to raise cash to then splash in the transfer market and West Ham are again keen.
However, behind the scenes, West Ham are not receiving encouragement about a possible move being able to happen.
Onana is likely to want to join a side playing Champions League football if he does leave Goodison Park.
Still just 21 years old, the Belgium international played in 33 of Everton’s 38 Premier League matches last term, getting booked on nine occasions.
West Ham got up close looks at him in both their league meetings with Everton, with Onana clocking the full 90 minutes in both.
