The 30-year-old is expected to leave San Siro this summer, with MLS side Orlando City long linked with a move for the player, having already tied up a deal for compatriot Kaka.
Robinho's former club Santos have also admitted that they would be keen to bring the player back to Brazil, though they stressed that the ex-Real Madrid forward would need to lower his wage demands.
Galliani has since revealed that offers from Brazil and Olympiakos have been received for the player and indicated that Milan are already pursuing replacements, with Alessio Cerci a reported option.
"There's no offer from Besiktas, there is something from Brazil and Olympiakos. We just finished a meeting and we will update tomorrow," he told Sky Italia on Monday.
"The market at the moment is geared towards a wide player if we part with Robinho. [Coach] Pippo Inzaghi wants left-footed players on the right side."
Galliani also underlined his determination to keep Mario Balotelli at the club and insisted that the team's defenders need time to adjust following the 5-1 thrashing at the hands of Manchester City.
"I'll update the chances of him staying to 99.999 per cent," he said of Balotelli, who has been the subject of interest from Arsenal. "I liked the way he played when he came on last night. He is our centre forward and will stay.
"Defeats are certainly not something to be pleased with. In defence the centre-backs need time to get into shape but Alex and [Adil] Rami are a great pair, as are [Daniele] Bonera and [Philippe] Mexes."
Galliani also declared his belief that Italian Football Federation (FIGC) presidential candidate Carlo Tavecchio is not a racist following his remarks on the influx of foreign players in Serie A.
"Tavecchio? It was certainly an unhappy joke but it ends there," he remarked. "Tavecchio's life has always been devoted to institutions, it's certain he is no racist and it was just a little joke."