While a number of names have been linked with a switch to the Premier League outfit, Milik is believed to be high on Mourinho's shortlist.
According to The Sun, club officials are discussing the possibility of signing the Poland international for a fee in the region of £25m.
With less than a year remaining on his contract, Milik will be allowed to leave the Italian outfit for the right price this summer.
The 26-year-old has played no part in Napoli's opening two matches of the season, a sign that he no longer features in Gennaro Gattuso's plans. body check tags ::