The pacey attacker is currently French football’s fourth highest scorer this term, and has been attracting interest from a host of top clubs of late.
Both Arsenal and Juventus have been linked with the 22-year-old in recent times, but the Reds are keen to win the race and have already contacted his representatives.
Lyon are by no means the same team that dominated Ligue 1 a matter of years ago and are currently gripped by financial worry.
As a result top players are expected to leave to ease the tension at the club, with Lacazette, arguably, their most valuable asset.
The player himself is also rumoured to be open to a big move, which could open the door for a switch to Anfield.
The Merseysiders are set for a big summer of transfer activity on the back of an impressive campaign, with manager Brendan Rodgers believed to have in excess of £60m to spend after securing Champions League qualification.