The Rossoneri have already bid for the France Under-21 international, who has admitted that he would find it difficult to reject the opportunity to move to San Siro
Rossoneri CEO Adriano Galliani revealed on Friday morning that the Serie A side had made an offer for the centre-back and that he intends to travel to France imminently to discuss the bid with the 23-year-old's current employers.
Yanga-Mbiwa, who has represented France at Under-21 level, has publicly expressed his interest in moving to San Siro, but Girard is hoping that Montpellier manage to hold on to the club captain.
"I do not want his departure," the coach confessed to reporters on Friday afternoon. "He has said many things in the press, but for now he is with us."
Milan are looking to strengthen their defence following the sale of Thiago Silva to Paris Saint-Germain and the departure of Alessandro Nesta to Montreal Impact.