The 20-year-old only joined the Toffees from Juventus last summer but has struggled to make his mark in English football, managing just one goal in 26 appearances in all competitions.
Everton are allegedly not prepared to sell the youngster despite the recent speculation, but according to Il Messaggero, Roma could attempt to test the Merseyside club's resolve.
The report claims that the Italian club are keen to sign a new striker during this summer's transfer window and have identified the Italy international as their leading target.
Kean, who has also been linked with Real Madrid, found the back of the net on eight occasions in 21 appearances for Juve before joining the Toffees ahead of the current season.
The forward's current deal at Goodison Park will run until the summer of 2024. body check tags ::