Both London clubs are looking to take the midfielder on an 18-month loan with an obligation to buy, reports Sky.
But the Blues are thought to be offering £55million for Fernandes, while the Hammers are said to be looking to pay £33million for the Portugal international.
Chelsea boss Frank Lampard has plenty of attacking options with the likes of Willian, Pedro, Callum Hudson-Odoi and Christian Pulisic.
And Lampard refused to discuss Zaha when asked at a recent press conference if Chelsea were pursuing a deal to sign the Ivory Coast international.
Lampard said: “I wouldn’t talk about Zaha and the idea of that deal is something I’ve never even considered. I won’t talk about Zaha because he’s not a player of ours.
“If we have to do business we’ll do it in the way that we see fit to try to make us better and that’s done behind closed doors as opposed to just announcing who we might want to bring in.”