The Frenchman has attracted the interest of both Barcelona and Atletico Madrid, with his agent meeting with Arsenal chiefs earlier this week.
There have been no bids for the 28-year-old yet this summer and the Gunners are thought to be preparing a new contract offer for the striker who scored 19 goals last season.
Arsenal fans will not want to see the France international leave and he appears to have put their minds at rest with an Instagram post at the clubs training ground at London Colney.
Lacazette wrote: 2 Years Now Am In @arsenal, I Just Want To Say Thank You To Everyone.. Thanks For All The Love And Strength U Give Me..
He also set the location of the post as My Home.
While a social media post is never an official announcement, the Frenchman certainly seems settled and happy at the Emirates as he prepares for a third season in north London.
Lacazette arrived at Arsenal in July 2017 for an initial fee of £46.5m and has scored 36 goals in 88 games in all competitions in the two seasons since.
The forward scored 13 Premier League goals last season, one less than the previous campaign, but also chipped in with an impressive eight assists.
The Gunners are struggling to get new signings completed this summer as they are operating with an extremely limited transfer budget compared to a number of their rivals.
Unai Emery is thought to have only around £45m to spend on new players and he has already