West Ham have pursued Giroud throughout the summer, and value the Frenchman at £20m, with a wage offer of £100,000-per-week over the course of a four-year contract on the table.
Sources at the Hammers have now confirmed that the club are “waiting for dominoes to fall” as they attempt to secure Giroud’s signature ahead of Everton.
The Toffees – who are spending aggressively in this transfer window – have also made their interest in the striker known to Arsenal, but West Ham believe he would rather remain in London than move to Merseyside.
Giroud's agent, Michael Manuello, meanwhile, maintains that his client has yet to make a decision over his future, telling Goal: "It is a private decision. We never say anything untill we decide."
With a deal for Giroud in the works, West Ham are also pursuing Manchester City striker Kelechi Iheanacho, with Slaven Bilic desperate to inject his squad with a dose of firepower.
Iheanacho has impressed in his limited time in the Manchester City starting XI, scoring four goals last season, but progress on a transfer has stalled, with Pep Guardiola’s side insistent that a buy-back clause is included in the deal.
West Ham remain wary of allowing City to turn the move into a “glorified loan”, but they are hopeful of making progress and will continue their pursuit even if they secure Giroud.
Such is their transfer strategy, West Ham have a number of other irons in the fire, and are also in contact with Chelsea over a potential move for Michy Batshuayi, though a deal is complicated by the likelihood of Diego Costa leaving Stamford Bridge this summer and the fact that the Blues would rather loan the striker out than sell him permanently.
Theo Walcott is another name under consideration, but he is valued at over £30m by the Gunners and West Ham may well be priced out of a deal.
However, Goal understands that Hernandez is keen to move to an elite European club after scoring 13 goals in all competitions last season, leaving the Hammers in a form of transfer limbo over the Mexican.