The France international has bagged 76 goals over the last three seasons, including 21 strikes in Ligue 1 during the 2015/16 campaign.
The Hammers hierarchy have made no secret of their desire to sign a top-class striker during the summer transfer window and according to LES, they recently launched a £26million bid for the 24-year-old assassin.
However, the offer has since been rejected, with rivaled interest from Barcelona and PSG driving up Lacazette’s price-tag to a whopping £39million.
It’s claimed the East London outfit are still considering an improved final offer but there are alternatives already on their radar – namely Marseille’s Michy Batshuayi and Liverpool front-man Christian Benteke.
Batshuayi is another who has been scoring for fun in the French top flight this season, notching up 17 goals in 36 Ligue 1 appearances.
Benteke, meanwhile, is being targeted as a potential loan signing, have struggled for game-time since Jurgen Klopp replaced Brendan Rodgers as Liverpool boss in October.