The Daily Mail says the Cameroon international was offered to the Hammers before their deal for Leicester City goalkeeper Mads Hermansen.
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But West Ham turned down United's proposal as they believed Onana wasn't any better than their No1 Alphonse Areola.
West Ham then swooped for Hermansen from the Foxes.
Both keepers have made errors this season, though Onana also made a mistake in his comeback game in United's Carabao Cup defeat to Grimsby in midweek.