The Rossoneri chief wants to bring in the midfielder soon but says that he can wait until January if CSKA Moscow do not drop their valuation
The Japan international has fewer than six months left on his contract at CSKA Moscow and has been heavily linked with a move to San Siro in the current transfer window.
Galliani insists that the Rossoneri have not given up on signing Honda but says that either his current Russian club must lower their valuation or that the Serie A side will wait until January to sign the player on a Bosman deal.
"The gift to the fans is Honda - we will only [sign] Honda at this moment in time," he told reporters at a press conference on Thursday. "The player wants to join Milan but we can’t overspend as he will be a free agent in four months.
"We’ll keep trying to sign him until we have to name our Champions League squad, then we’ll abandon the chase. We have made an offer and if they decrease their expectations then Honda will arrive at Milan. Let’s hope so…"
Milan are currently in the midst of pre-season ahead of the start of the new Serie A season on August 24.