The Hammers are desperate to improve their attacking options this summer and have already made several failed moves for strikers, but have had better success in their pursuit of Mexico international Hernandez.
The east Londoners are reported to have activated the £13m release clause in his Bayer Leverkusen contract and have held preliminary talks over a return to the Premier League after the 29-year-old spent five years at Manchester United previously.
The main sticking point for a deal could be Hernandez's wage demands, with the striker having asked for wages in the region of £140,000 per week.
West Ham are trying to offer Hernandez certain bonuses to complete his pay packet after baulking at the suggestion they would be willing to stump up £140,000 per week.
Chelsea are also believed to be interested in the Mexican and are likely to be willing to offer him the cash he wants.