Milan are attempting to agree a fee with CSKA for the Japan international.
"The gift to the fans is Honda, it can only be Honda at this moment in time," said Galliani.
"The player wants Milan, but we can't exaggerate 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 "