The AC Milan chief says the club is assessing potential signings to replace the Brazilian but insists Mario Balotelli will not be leaving San Siro.
The 30-year-old is expected to leave San Siro this summer, with MLS expansion 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 has also said it would be keen to bring the player back to Brazil, though it stressed 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 Milan is already pursuing replacements, with Alessio Cerci a reported option.
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"There's no offer from Besiktas, there is something from Brazil and Olympiakos. We just finished a meeting, we will update tomorrow," he told Sky Italia. "The market at the moment is geared towards a wide player if we part with Robinho. [Head 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 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. "I liked the way he played when he came on last night. He is our center forward and will stay. Defeats are certainly not something to be pleased with. In defense, the center 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 insisted Italian Football Federation (FIGC) presidential candidate Carlo Tavecchio is not a racist following his remarks on the influx of foreign players in Serie A.
"It was certainly an unhappy joke, but it ends there. Tavecchio's life has always been devoted to institutions, it's certain he is no racist and it was just a little joke," he added.