The French ace has been in excellent form this term, netting an impressive 13 goals in 25 Ligue 1 outings.
His top displays have alerted Brendan Rodgers, who is said to have had scouts assessing the 22-year-old over the course of the past few months.
Despite his side having found the net more than any other Premier League outfit this term, the Northern Irishman is still keen to bolster his front line and provide Luis Saurez and Daniel Sturridge with support and cover ahead of what is looking likely to be a season in Europe next term.
Although one of Lyon’s top performers, Liverpool are hopeful that an opening bid in the region of £10m will be enough to land Lacazette, with the French club known to be a state of financial worry.
The player himself is said to be keen to try his hand in England, which could smooth the process for the Merseyside club.
Arsenal and Tottenham are also watching Lacazette – who is able to play as a centre-forward or in a wide attacking role.