The Rossoneri have expressed their interest in the 23-year-old, who captained his side to Ligue 1 triumph last term, and could replace Thiago Silva at San Siro
The seven-time European champions last week sold the Brazilian international to Qatari-owned Paris Saint-Germain for €46 million, and are now looking to acquire the Frenchman to shore up their defence.
Yanga-Mbiwa skippered Montpellier to a surprise Ligue 1 triumph last season, with his burgeoning reputation earning him a call-up to France's preliminary Euro 2012 squad before being cut from the final 23.
The Rossoneri have already signed Francesco Acerbi from Genoa, but the club is understood to be looking for further reinforcements, with Yanga-Mbiwa thought to be the preferred choice for Massimiliano Allegri.
It is also believed that Adriano Galliani is monitoring FC Porto's Rolando as the Serie A runners-up look to compensate for the departure of Alessandro Nesta.
Yanga-Mbiwa has a valuation of around €6 million, with the 23-year-old having entering the final year of his contract.