Angry supporters, who want the club to keep the Brazil playmaker, chanted and held up banners in the pouring rain while blocking a main road outside Milan's city centre offices.
Media reports have said Premier League City, the richest club in the world after their takeover by Abu Dhabi United Group, have bid a world record 110 million euros ($146 million) for the 26-year-old.
Galliani met club owner and Italian Prime Minister Silvio Berlusconi before holding talks with Kaka's father.
"There is no news," coach Carlo Ancelotti told reporters.
Milan have said they will take their time to consider the bid and that no decision has been made by the club or the player, whose Milan contract runs until 2013.
Italian media have said Kaka does not want to go to City but that the transfer could still go through. The Brazilian was chased by Real Madrid last year and Milan acknowledged his father held talks with the Spanish club.
