The Japan international is keen to link up with the Rossoneri this summer but CSKA's high asking price for the 27-year-old has now put the transfer on hold for at least the next five months.
Galliani told reporters that unless Milan can raise funds from external sources, the club will pursue Honda when he becomes a free agent.
"Honda's contract expires on December 31st and he can open up negotiations with other clubs, like us. I think he will arrive in January," said Galliani.
"I don't think he will arrive now unless some sponsor allows the move to take place.
"His price tag and his wages are just too high but if an external source were to intervene, then it could happen."