According to Gazzetta dello Sport (via Football Italia), Milan - who were recently banned from competing in next season's Europa League for breaching Financial Fair Play rules - will bring Zaza in on an initial loan deal, with an obligation to sign the player for €20m next summer.
Kalinić will need to leave the club before a deal can be struck, in order to ensure that I Rossoneri can balance the books.
After joining the club on a permanent deal from Juventus, the Italian international went on a prolific goalscoring run, finishing the 2017/18 season with an impressive tally of 19 goals in all competitions.
Zaza, who grew up supporting Milan, is believed to have already agreed a four year deal worth around €2.5m with the San Siro side, and will be eager to impress in Italian football after failing to play to his full potential with previous spells in his home nation. Kalinić is likely to join Atléti as an extra option upfront, after scoring just six times during his loan spell with Milan.
Kalinić was due to sign for Milan this summer, as I Rossoneri had the option to bring in the Croatian beanpole on a permanent basis, but they are unwilling to complete the deal given his woeful 2017/18 campaign with the club.
The 30-year-old has also had a summer of controversy, after being sent home form the World Cup after refusing to appear as a substitute for Croatia.
In other news, Lyon winger Memphis Depay has added fuel to the fire of rumours suggesting that he's set to join Milan this summer, after missing a training session with the Ligue 1 side. The former Manchester United man has been strongly rumoured to be plotting a move to the San Siro, and his tenacious style of play could be what Milan need to improve next season.