The defender has been earmarked as a potential replacement for Thiago Silva, who quit San Siro in favor of a move to Paris Saint-Germain last month.
The Rossoneri has bid 6 million euros to land the highly-rated defender, who starred as the club secured a shock league triumph in the 2011-12 season.
Montpellier president Louis Nicollin had last week laughed off rumors of a Milanese bid, referring to chief executive Adriano Galliani as "Kojak", before dismissing any foreign interest.
The Italian giants were earlier reported to have set a deadline of this weekend to try and entice the Bangui-born center back to Lombardy, before seeking alternatives.
The report in Gazzetta states that the situation has changed, with Yanga-Mbiwa privately asking for Montpellier's blessing to sanction the move, as Milan remains cautiously optimistic of a signing.
Though La Paillade has not treated the plea as a formal request to leave, it remains to be seen whether a deal will be negotiated before the deadline.
Montpellier commences the defense of its Ligue 1 title on Friday against Toulouse.
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