Lacazette, 23, was linked earlier this year with Arsenal but no approaches have been forthcoming and he stated earlier this month that he isn’t looking to quit Lyon.
“I have not expressed any desire to leave, so for me it is obvious to stay at the club and continue with the project.”
Lacazette has 15 goals and four assists in 18 matches so far this term. Last season he scored 15 goals in 36 games.
The Daily Mirror claims Liverpool want him to replace the misfiring Mario Balotelli. The Italian has failed to score in the Premier League this season and faces a ban of up to five games after pleading guilty to a charge connected with a posting on Instagram.
Lyon president Jean-Michel Aulas recently stated that he has no desire to part with Lacazette, saying: “It would be stupid to cut the dynamics by selling the centrepiece of the team.”
A move to Liverpool looks unlikely unless the Premier League side offer a huge fee.