The Belgium international, 20, is expected to sign a five-year deal upon complete of a medical after the Toffees agreed a £33.7million fee with the Ligue 1 club.
Everton are also close to agreeing a deal to bring former midfielder Idrissa Gueye back from Paris Saint-Germain.
While manager Frank Lampard is closing in on a stronger midfield, he remains desperately short up front.
Richarlison joined Tottenham earlier this summer and Dominic Calvert-Lewin is out for six weeks, leaving Salamon Rondon - who is supended for the opening match against Chelsea - as the club's first-choice striker beyond Saturday.
West Ham manager David Moyes is also feeling thin on the ground despite landing a fifth summer signing in Maxwell Cornet from Burnley.
Nayef Aguerd, Flynn Downes, Gianluca Scamacca and Alphonse Areola have also signed, but Moyes wants more after losing out on Onana.
"We've made good signings. We've had one or two injuries as well, which we have to take into consideration, but we're far from finished in that regard," said Moyes.
"We lost three outfield players and a goalkeeper this summer.
"We didn't bring any players in during January so we need to fill these voids.
"We want to bring in quality players and we're working to do that."