The Rossoneri director also confirms that his club have been in discussions with Fiorentina over the potential purchase of their Serbian midfielder, 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 nearing its close, Galliani admits 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," the Rossoneri chief 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 that there had been contact between the two clubs.
"Ljajic? I met with [Fiorentina sporting director Daniele] Prade [on Wednesday] morning," he confirmed.