The 25-year-old has been in scintillating form over the past three seasons, scoring more than 70 league goals in that time including 24 in just 27 appearances so far this term.
Lacazette has been regularly linked with a move to the Premier League in that time, and RMC claims that Liverpool have now joined the race to sign him.
The club are understood to have a long-standing interest in the France international and have been monitoring his progress over the past three years.
However, the Reds are likely to face competition for Lacazette's signature from the likes of Arsenal, Borussia Dortmund and Atletico Madrid, the latter of whom are thought to be favourites to win the race.
Lyon have already confirmed that they will not stand in Lacazette's way should they receive a substantial bid for the striker this summer.