The seven-time European Champions 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.
The exits of sporting director Mirabelli and Fassone have created a gap in the club’s hierarchy, and according to reports in England and Italy Gazidis is the man they want to replace Fassone.
Arsenal were quick to refute any speculation though, releasing a statement on Wednesday morning. It read:
‘We are aware of the speculation surrounding our chief executive Ivan Gazidis. We know he receives many offers from organisations inside and outside the game as he’s a hugely respected figure.
‘He has never accepted any of these opportunities and has never spoken about them publicly. He has always been fully committed to taking Arsenal forward and is currently working hard in Singapore with our new head coach Unai Emery as we prepare for the new season.’
All this has come about following the arrival of Elliott Management, who took over from the beleaguered Li Yonghong this summer.
Paolo Scaroni was appointed as executive chairman in one of the first behind-the-scenes changes, but it now appears certain that plenty more will follow.