The centre-back, 24, is co-owned by Genoa and impressed this season as the Flying Donkeys comfortably avoided relegation by finishing 10th in Serie A.
It was his first season in the top flight but his performances have led to interest from a Milan side looking to rejuvenate their ageing squad, with Alessandro Nesta one of many players to leave this summer.
"I hope to join Milan," Acerbi told TMW. "It would be a dream come true. I’m just waiting for my agent to tell me to sign.
"Milan are a really strong team, with many great players. You can only be flattered by such interest.
"Over the past few months I have shown that I am a Serie A player but, to be honest, I never thought I’d end up at Milan."
Acerbi started life as a semi-professional player with Pavia, and played for Serie B Reggina for a season before joining Chievo last summer.
He joined the Verona-based side in a 50 per cent rights deal with Genoa, who signed midfielder Kevin Constant in return.
The 6”4’stopped did not break into the first team initially but, since the winter break, has become an ever-present, starting 14 matches, more than any other defender.