The Hammers are desperate to bolster their frontline, having eyed an array of players this summer.
Interest in the likes of Arsenal’s Olivier Giroud and Manchester City’s Kelechi Iheanacho has since ended.
That has left Hernandez as Bilic’s No1 striker target to solve West Ham’s issues up front.
The Bayer Leverkusen star, who has a £13million buy-out clause in his contract, is open to returning to the Premier League.
And Chelsea have also been tracking the former Manchester United goalscorer.
Bayer Leverkusen striker Javier Hernandez could become West Ham's highest-paid player
The Hammers have spoken to Hernandez’s representatives
According to Mexican newspaper Publimetro, the Blues voiced their interest in the 29-year-old with Antonio Conte also needing strikers at Stamford Bridge.
But the Hammers have spoken to Hernandez’s representatives.
And it appears a move to the London Stadium could be on the cards.
The Sun claim West Ham would make him their highest-paid player on a £145,000-a-week contract.
West Ham United transfers: Which stars are most likely to sign? Mon, July 10, 2017
Which transfers are West Ham United most likely to complete this summer, according to Football Whispers (1 – unlikely, 5- very likely)?
Play slideshow West Ham United via Getty Images 1 of 11
Get Quotes on Home Insurance
Who are West Ham United most likely to sign during the summer transfer window?
Hernandez would lead their line, and Slaven Bilic has the added advantage of being able to guarantee ‘Chicharito’ regular game time, which is unlikely to be the case at Chelsea.
With West Ham stepping up their attempts to sign Hernandez, they are making progress in other areas too.
Manchester City Joe Hart is set to complete a loan move today, while a third bid is expected for Stoke winger Marko Arnautovic, who wants to join.
Chelsea, meanwhile, want Pierre-Emerick Aubameyang as they seek a world-class striker to replace Diego Costa.