The Rossoneri had been in negotiations with CSKA Moscow but Yevgeny Giner's €5m (£4.3m) demands have proven too rich for the Serie A outfit.
However, Galliani said that coach Messimiliano Allegri may yet receive "a gift" before the transfer summer window shuts in September.
"There is no chance for Honda," Galliani told Milan Channel.
"The president of CSKA is on holiday, and there are no meetings planned with the Della Valle family this weekend either - but let's see if the coach doesn't get a gift anyway."
Honda has agreed a pre-contract with Milan, which will see him join the club in the January transfer window.