Lacazette, 24, has been one of the most prolific strikers in Europe over the last three seasons, and his 20 goals this season mean it's now 73 goals since the start of the 2013-14 season; a quite remarkable record.
Now, West Ham are believed to be keen on bringing Lacazette to East London this summer, as manager Slaven Bilic is seemingly desperate to splash the cash on a proven goalscorer this summer.
Lacazette would certainly provide that, but with bigger clubs around Europe no doubt keen on him, it will be difficult for West Ham to fend off the competition, even with the Olympic Stadium and the new Premier League TV money on offer this summer.
However, they may yet have one trick up their sleeve. Le10 Sport reported back in March that Bilic had sent West Ham star Dimitri Payet to speak to Lacazette in a bid to convince him that a move to West Ham is the right one for the striker to make.
Payet is a French international team-mate of Lacazette, and the two have played alongside each other on a number of occasions, with a link up at this summer's European Championships far from out of the question.
Payet only joined West Ham from Marseille last summer, but has become a hero at the club already, dazzling fans with his incredible skill and technique - leading fans of many other clubs to wonder just why a bigger club than West Ham didn't sign him.
With Payet's experiences to lean on, West Ham have a real selling point to Lacazette; become a fan favourite and West Ham and fire the club to Europe, rather than go to one of the so-called 'big clubs' in the Premier League and be a bit-part player.
It's still an ambitious move, but with Payet on their side, it may be a plan that could work for West Ham as they look for bigger and bigger names in the transfer market.
Would you want to see Payet and Lacazette link up at West Ham?