The Milan director also admitted that his club had been in discussions with Fiorentina over the potential purchase of Adem Ljajic
The Brazilian forward has been in talks over a move to Santos this summer but differences over the fee and the player's potential salary have caused negotiations to grind to a standstill.
With the transfer window in the South American nation closing in just over a week, Galliani has admitted that the former Real Madrid attacker's future hinges on whether a deal is struck soon.
"The Brazilian market closes on July 20, so by that date either Robinho will go or he is staying. The negotiations are continuing without any substantial developments," Galliani told reporters on Wednesday.
If the 29-year-old does depart, an attacking replacement could arrive at San Siro in the form of Fiorentina's Adem Ljajic, with Galliani admitting there had been contact between the two clubs.
"Ljajic? I met with [Fiorentina sporting director Daniele] Prade this morning," added the Rossoneri chief.