The Serie A club are looking for €40M (£36M) for the 19-year-old and also want a buy-back clause inserted into any deal.
Following the departure of Ademola Lookman to RB Leipzig, the Toffees are looking to bring in another forward and the Italian international is seen as the perfect fit.
Talks are believed to be ongoing for a player who scored six Serie A goals in 13 appearances last season and has also played three times for Italy, scoring twice.
Everton are also keen to sign Crystal Palace winger Wilfried Zaha and are said to be preparing a £60m bid for the Ivory Coast international, who has been valued at nearer to £80m by the Eagles. The Merseyside club are understood to be willing to offer a player as part of any deal.
Zaha, who has also been a target for Arsenal, would prefer to remain in London this summer, but he is understood to be willing to move back to the north-west – where he had an unsuccessful two-year spell at Manchester United.
The Gunners have had a £40m bid rejected already this summer, but they now appear to have put their pursuit of Zaha on the back-burner after agreeing a £72m fee with Lille for winger Nicolas Pepe, according to Sky in Italy.
Zaha has told Palace he wants to leave and is keen to secure his dream move to Arsenal – the club he has supported since he was a child.
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