The 38-year-old is a free agent ahead of the January transfer window after leaving Los Angeles Galaxy in November following two seasons with the Californian side.
According to Area Napoli, the Toffees have made contact with Ibrahimovic's agent, Mino Raiola, about a potential move.
The Swede is keen to make a return to Italy but is aware of the fact that he still has admirers in the Premier League following his impressive 2016-17 season at Manchester United.
Speaking earlier this week, Raiola indicated that Zlatan moving to Italy was by no means a foregone conclusion. body check tags ::