The 29-year-old former Manchester City and Real Madrid forward was close to agreeing a move to his boyhood club in January, having spent six months back in Brazil on loan from City in 2010.
Terms could not be agreed, however, and Robinho completed the Serie A season with Milan.
However, Galliani has confirmed the transfer - which would net the Italians a reported eight million euros - is back on and the Rossoneri are lining up a possible replacement.
He told the Corriere dello Sport: "Last night we sent our latest proposal to Santos. The player has even accepted a reduction to his wages. If Robinho leaves, another striker will need to come in."
Galliani, who revealed his disappointment at missing out on Juventus-bound striker Carlos Tevez last week, would not identify a preferred reinforcement to his forward line but hinted CSKA Moscow midfielder Keisuke Honda could be a worthy addition to the San Siro midfield.
A deal for Sampdoria's young Italy midfielder Andrea Poli, meanwhile, requires defender Bartosz Salamon to agree to move in the other direction.
"Honda? I consider him to be an excellent attacking midfielder," Galliani said.
"(Poli's) arrival is certain, he's finished his medical and I'll be having dinner with him tonight. A good omen is that he has the same September 29 birthday as (Silvio) Berlusconi and (Andriy) Shevchenko.
"But the time when we can make it official depends on an agreement between Sampdoria and Salamon."