That's according to Calciomercato's Fabrizio Romano, who reported Juventus are monitoring the 16-year-old, and Bianconeri CEO Giuseppe Marotta is an admirer of the youngster.
United, Chelsea and PSG are among the other interested parties, but Inter Milan "have slowed down their pursuit of him considerably after negotiations came to an abrupt halt last summer," while AC Milan will struggle to meet Genoa's demands as they want at least €40 million for the precocious talent.
The striker, who already possesses a 6'4" frame, made his debut in Serie A last season at the age of just 15.
After a pair of brief cameo appearances against Torino and Chievo, Pellegri started against Roma in the final game of the campaign.
As noted by Serie A expert James Horncastle, he made quite the impression during the match and again in his first appearance this season against Lazio:
He set another record in the Italian top flight with his brace, per OptaPaolo:
However, the youngster is yet to score since and has played just 30 minutes after that game, having spent time on the bench and on the sidelines with injury.
It's still early in Pellegri's career and a big-money move would likely do him no favours at this point, and likewise it would be a lot to gamble on someone so unproved even for Europe's wealthier outfits.
It stands Juventus in good stead if they're at the forefront of the queue to snap him up at some point down the line, though, as he has the potential to be a future star in Italy.
He has much to do in terms of developing or proving himself in the meantime, but it's of little surprise Europe's elite are already taking a keen interest in him.