Reports in the British media have claimed Manchester City, Liverpool and Arsenal are among the Premier League clubs keen on the French forward, who tops the Ligue 1 scoring table with 17 goals this season.
Lyon president Jean-Michel Aulas declared late last month he has no interest in selling Lacazette, who is on contract until June 2018, while the 23-year-old striker is keen to help the seven-time French champions back to the top of the league.
Lyon have not played in the UEFA Champions League since 2011-12 but will qualify again if they maintain their current position of second in Ligue 1, while they have not been crowned champions since 2007-08.
Aulas is banking on academy graduates like Lacazette to give Lyon success again.
Lacazette is committed to that project.
"The system was put in place a while ago but the economic context may mean some people have to leave," the striker conceded after Lyon's Coupe de France win on Sunday.
"If we're no longer all together, we certainly won't have the same collective strength. As for me, if the club can continue to allow me to improve, why shouldn't I stay?"
