The Hammers have reportedly drawn up a three-man striking shortlist, as they look to improve their attacking options for next season.
West Ham are believed to have identified Lacazette, along with Liverpool striker Christian Benteke and Marseille forward Michy Batshuayi as their ideal summer signings.
The Hammers only want one of the trio, but they will apparently submit three bids and see which move can be completed the most quickly.
What could be crucial, is that Lacazette is said to fancy a switch to the Olympic Stadium.
The French international is eager to test himself in the Premier League and a move to West Ham is an exciting prospect for him.
Lacazette has slammed in 23 goals in 43 appearances for Lyon this season, and he has been one of the most prolific strikers in Ligue 1 for a sustained period of time.
West Ham had great success buying from France last summer, with the addition of Dimitri Payet widely being recognised as their best signing in years, and Lacazette will hope to have a similar impact if he does make a switch to the London club.