Milan had been hoping to secure a deal for the playmaker, who won Serie A and the Champions League in a six-year spell with the Rossoneri before leaving for Real Madrid in 2009.
However, Galliani says he was unable to come to a financial agreement with Madrid. It is reported Milan wanted Kaka on loan while Madrid would only consider a permanent deal.
"The negotiation has failed," Galliani said. "We have given up due to the fiscal situation.
"Kaka made every possible effort but everything has failed due to the fiscal situation that convinced Real to stop the negotiations.
"At this point, I think we will remain as we are."