The Partenopei are in the market for a new forward following the loss of talisman Gonzalo Higuain to rivals Juventus.
According to Sky Sport Italia, Milik is set for a medical ahead of a €35 million move.
A deal for Icardi is further away with the Nerazzurri reluctant to sell with the Partenopei reportedly willing to offer €45 million plus Manolo Gabbiadini for the 23-year-old.
Inter’s sporting director Piero Ausilio is expected to consider the offer during the team’s tour of the United States of America along with the Suning group.
Napoli are willing to look elsewhere if their Serie A rivals fail to offer a response but they are reportedly becoming increasingly optimistic that their offer could be expected.