The 16-year-old burst onto the scene last season when he became the youngest scorer in Serie A history after finding the net against for Genoa against Roma in May.
Big sides are now looking to lure the striker away from his boyhood club and he recently had a tour of AC Milan's training ground.
Manchester City were another club after Pellegri but, according to Calciomercato, he has rejected their approach.
The teenager reportedly wants to continue his development at Genoa for now and has no plans to leave.
For that reason, Pellegri has also snubbed Milan's offer and may even hold talks over a new deal soon.