The chief executive spoke ahead of the last 16 tie against Atletico Madrid and said his club's European record always plays in its favor.
The first leg of the last 16 tie will take place at San Siro on Wednesday evening, and Gallaini hosted Atleti dignitaries at a lunch at the Giannino restaurant.
“We have a great Champions League tradition. In the last 13 years, we have been in it 11 times and always got past the group stages," the Milan executive told Sky Sport 24. “Our coach Seedorf is very concentrated on the challenge. Since he was 18 he has been playing in the Champions League. Atletico Madrid will be tough opposition. They won their Champions League group and are joint top of La Liga.
“Tomorrow will be the 28th anniversary of Berlusconi taking over Milan. We have had some great teams. In 2007, when I saw the rain in the semifinal against Man Utd, I knew it would be a beautiful game. We hope to return to those levels. Will Kaka be captain against Atletico? He is certainly a great leader, but I don't know.”
Galliani also spoke of his confidence that Mario Balotelli will improve and reach the highest level of the game, while also praising another former Milan star, Zlatan Ibrahimovic, who scored a double in Paris Saint-Germain's 4-0 thumping of Bayer Leverkusen on Tuesday.
“Balotelli has everything in order to become a great champion. He is still very young and growing. He has all the physical and technical qualities to become a top player," he continued. "I saw Ibrahimovic yesterday. He is extraordinary.”