Reports in France claim Liverpool and Arsenal are tracking the 22-year-old, who has scored 17 goals for Lyon this season.
Lyon are reluctant to lose Lacazette, but are braced for big-money offers for the forward this summer.
The 22-year-old has suggested he would consider a move away from Lyon if the right offer came long.
"I'm tempted to try and experience life abroad," Lacazette is quoted as saying in The Sun.
"Are Arsenal and Liverpool interested? An experience in another major league fascinates me."