There have been conflicting reports over recent days as to the San Siro giants' chase of in-demand Real Madrid star Alvaro Morata, who has also been courted by the likes of Manchester United and Chelsea this summer.
Chelsea manager Antonio Conte wants to sign Juventus striker Gonzalo Higuain.
Andrea Belotti is said to be one of Chelsea's targets to replace Costa after his stunning performances for Torino last term.
While several sources insist that a deal to take the Spanish global to Milan is nearly a done-deal for 70 million Euro plus bonuses, other outlets claim that Los Blancos are still extremely resistant to sell, especially with Monaco starlet Kylian Mbappe looking increasingly likely to remain at the Stade Louis.
The addition of Belotti to their ranks could see them challenging for the Serie A title, a title they haven't won since 2010/11.
Juventus have already sold key defender Leonardo Bonucci and have no intention of selling a key element from the offensive department.
And CalcioMercato claim they are willing to try their luck with a move for Belotti who is reportedly keen on the move.
But according to Calciomercato, the 23-year-old forward wants to join Milan having been swayed by their ambitious project, with the club making eight new signings this summer.
"I thought that considering the type of qualities Costa has, that Belotti was the flawless fit".
The Italian striker has been on the lips of Europe's top clubs over the past six months after scoring 40 goals in 74 appearances for mid table Italian club Torino.