The 20-year-old struggled to settle at Everton last season and was loaned out to Paris Saint-Germain in the last window, where he has proven himself.
He has scored nine times in 16 appearances for the French champions and has been showing the talent that convinced Everton to pay £27m to sign him from Juventus in 2019.
There are already suggestions that PSG are looking to turn the loan into a permanent deal and are considering holding talks with Everton soon.
But it has been claimed that Everton are only likely to sell him if they receive a big offer for the striker as they feel he has a future at Goodison Park.
Ancelotti has suggested that he expects his countryman back at Everton next season despite his previous struggles and remains a fan.
Everton director of football Marcel Brands also has much invested in Kean and is likely to bat to keep him at the club for the long term.
There are suggestions that PSG could offer around £31m for Kean to sign him on a permanent deal from Everton.
It remains to be seen whether that would be enough to convince Everton as it would only represent a small profit from Kean’s departure.
And it is also unclear what Everton would do if Kean pushes to leave.