The 30-year-old, who was strongly linked with a move away from the Emirates Stadium over the summer, has less than a year remaining on his current contract.
According to Calciomercato Lacazette is unlikely to renew his deal with the Gunners as he wants to join a club competing for trophies at the highest level.
La Liga duo Atletico Madrid and Sevilla are both understood to have expressed their interest signing the Frenchman on a free transfer, while Juventus and AC Milan are considering a potential move for him in January.
Despite speculation surrounding Lacazette's future, Arsenal head coach Mikel Arteta is keen for the striker to stay and has stated that he will be "instrumental in our success."
Lacazette ended the 2020-21 campaign as the North London club's top goalscorer, finding the net 17 times in 43 games across all competitions.