Meanwhile, Robinho is edging towards a January return to Brazil.
Reports in Brazil and Italy have linked Pato with a possible move to recent Club World Cup winners Corinthians in the transfer window, with fellow Campeonato Brasileiro side Santos publicly declaring their willingness to bring Robinho back to his boyhood club.
Galliani is eager to retain the latter but admits persuading the forward to stay in Italy will be a tall order.
He told the Corriere dello Sport: "Milan have received an offer for Pato.
"Meanwhile, I am doing everything in my power to keep Robinho, I don't know if I will succeed, but I will use all my powers of persuasion.
"Robinho is happy here. He has a good relationship with the coach and the team, but he has a wife and children who are back on the beaches of Santos right now.
"I hope to convince him to stay here. He hasn't asked vehemently to leave Milan, he's just asked to go back to his country."
The potential departure of a strike partnership that cost the Rossoneri a combined 30 million euros could free up space for long-term target Mario Balotelli, but Galliani would not be drawn on the Manchester City striker today.
"If both Robinho and Pato leave, we will only buy one striker because we believe the right number of strikers should be five," he added.
"Is (Didier) Drogba possible? No. (Javier) Pastore? No, because we've asked Paris St Germain and they won't let him go."
Robinho, who originally left Santos to join Real Madrid in 2005, arrived in Milan following an unsettled two-year spell with Manchester City, but not before spending six months on loan back at Vila Belmiro in 2010.
Santos vice-president Odilio Rodrigues told UOL Esporte: "We are in negotiations. It will be difficult but we are are doing everything in our power to realise our fans' dream."