The San Siro outfit are under new ownership and have already sacked two of their biggest names behind the scenes in a huge summer shake-up.
Sporting director Massimiliano Mirabelli and chief executive Marco Fassone were dismissed this week, and it now appears Gattuso could be the next to leave.
Conte is out of work following his departure from Stamford Bridge this month, and would be an obvious choice given his previous time in Serie A with Juventus and others.
AC Milan came sixth last season and appear to be taking no prisoners in their battle to return to the top table of Italian football.
One other potential arrival this summer is Arsenal chief executive Ivan Gazidis, who is wanted to replace Fassone at the San Siro.