Fininvest - a holding company owned by ex-Italian Prime Minister Silvio Berlusconi - currently has a 99% stake in the club.
Ma and co-investors would purchase 70% of Fininvest's shares straight away, La Repubblica says, then buy the remaining 30% "within a year."
Ma, worth $23 billion (£15.8 billion) according to Forbes, also owns a 40% stake in Chinese football team Guangzhou Evergrande Taobao.
It's the first club in China's history to win AFC Champions League twice - in 2013 and 2015.
AC Milan finished outside the top 10 of the Deloitte Money League rich-list for the second time in the 2014/15 season, with revenues of €199.1 million - one of the only major clubs to have a revenue decline that year. This was partly down to not qualifying for any European competitions, with TV and attendance revenue falling as a result.
Alibaba did not give confirmation of the takeover at the time of publication, but Business Insider will update the story as it develops.