The 23-year-old is said to be privately pushing through a move to the Italian giants, and has asked his current side to allow him to leave in this transfer window
The defender has been earmarked as a potential replacement for Thiago Silva, who quit San Siro in favour of a move to Paris Saint-Germain last month.
The Rossoneri have bid €6 million 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 rumours 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 centre-back to Lombardy, before seeking alternatives.
La Gazzetta dello Sport state that the situation has changed, with Yanga-Mbiwa privately asking for Montpellier's blessing to sanction the move, as Milan remain cautiously optimistic of completing a deal.
Though La Paillade have 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 commence the defence of their Ligue 1 title on Friday against Toulouse. Kick-off is at 20:45 CET.
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