The 43-year-old is said to have been impressed by the Hammers' ambition and their impending move to the Olympic Stadium.
Slaven Bilic, who has left Turkish side Besiktas, remains the bookies' favourite for the Hammers hotseat.
But the Irons received a timely boost on Sunday night when Napoli's defeat in an unofficial Champions League "play-off" match against rivals Lazio saw them denied a place at European football's top table next season.
Had the Italians qualified it could well have swayed Emery's decision over the next step in his impressive career so far.
But now the Azzurri will be joining the Hammers in the Europa League the lure of the Premier League and West Ham's project could prove pivotal for the former Valencia and Spartak Moscow boss.
Emery certainly fits the profile desired by co-owners David Sullivan and David Gold, who have said they want to bring in an "exciting" manager with a philosophy and brand of football true to the club's roots.
His more European, passing style would certainly do that, although the language barrier could prove an issue initially.
Emery made his name by guiding minnows Almeria into La Liga before moving to Valencia, where he qualified for the Champions League in three successive seasons.
He had an unsuccessful spell in Russia before returning to Spain where he was won the Europa League twice, in successive seasons, with current club Sevilla who also finished fifth in the top flight in both years.