The Rossoneri vice-president believes a deal could be done for the Real Madrid midfielder, but says there are still financial barriers to overcome if the Brazilian is to return
The midfielder's time at the Santiago Bernabeu has not gone according to plan and with the Rossoneri themselves enduring a tough campaign, the player and club could be reunited.
However, the Italian side's vice-president insists a deal can only be done if financial barriers are overcome before the end of the January transfer window.
"I'm more pessimistic than yesterday, it's very hard but we'll still try to sign him," he told reporters."The negotiation isn't easy due to Kaka's wage. No one in Italy can pay a €5million [£4.2m] salary."
"He must make sacrifices to come back to Milan."
Galliani also believes a move would help Kaka's international career, and stand the player in good stead before the 2014 World Cup, hosted in his home nation of Brazil.
"AC Milan would be a good showcase for the World Cup, and there are 15,000 fans here who haven't been seen since Kaka left."
Milan manager Massimiliano Allegri also spoke about the possibility of bringing the Brazil international back to Italy and denied claims he was against the transfer.
"There are talks in progress for Kaka, an important negotiation process if this great return is to occur," he told reporters.
"I agree with the club and Adriano Galliani on everything, so my position has never been opposed to that of the club. There is an exchange of ideas, certainly, but it’s not true that I don’t want Kaka."
Allegri did, however, rule out the prospect of bringing David Beckham to the club, joking that it was impossible to "wipe out the player's birth certificate" in relation to their new youth-orientated recruitment policy.