The Slovakian midfielder has been a long-term target for the Rossoneri and he is widely tipped to join the club in the summer transfer window.
Milan and Genoa have done a lot of business of late, and they are currently putting the final touches on the agreement that will see Kucka move to San Siro next summer.
With veteran midfielder Massimo Ambrosini expected to leave at the end of the season, Milan officials believe the Slovakia international would be a perfect addition to the centre of the park.
The 26-year-old joined Genoa from Sparta Praha in January 2011 and quickly developed into an important member of the squad at Stadio Luigi Ferraris.
He has made a total of 69 Serie A appearances for the Rossoblu, and has scored 5 goals in the process.