The summer saga seems to be drawing to a close with the player's representative and brother, Hiroyuki, confirming an agreement could be reached in "an important week" of talks
The Japan international has long been linked with a move to the San Siro giants, but the clubs have not reached an agreement over a possible move for the player so far.
And Hiroyuki has now confirmed that a switch only depends on the two sides settling on a transfer fee this week.
"It all depends on the two clubs, just them," he told TMW.
"There is no need for me to speak with CSKA again. They already know the situation from the player’s point of view.
"This will be a very, very important week. Milan will see CSKA and there could be developments before the weekend.
"Keisuke is calm. The hope is that he can join Milan now, but all we can do is wait and see."
Adriano Galliani feels Milan are close to securing the 27-year-old's signature, but they are prepared to wait until December when the players contract expires to wrap up the deal.
"We are pretty relaxed when it comes to Honda," the club's vice-president told reporters on Monday.
"We cannot sign players who are not for sale. If CSKA Moscow do not want to sell then we will wait patiently."
The Rossoneri have also been chasing Fiorentina's Adem Ljajic but the Viola are unhappy with the way the club are pursuing their star man.