The Rossoneri finished 10th in Serie A season, with their failure to qualify for European competition resulting in the dismissal of Filippo Inzaghi after just one year at the helm.
Mihajlovic was promptly hired to fill the void, after leading Sampdoria to a sixth-placed finish, and Galliani believes he is similar to the Italian coaching icon who won four Scudetti and one Champions League title at San Siro.
"To me, Sinisa seems really similar to Capello," the Rossoneri vice-president told reporters on Friday. "But then, it's clear that every coach has his own story.
"But from what we've seen in pre-season in China, we can have great hope for the future. We've seen a great Milan up until now. We're all happy."
Mihaljovic has enjoyed an encouraging start to his tenure - Milan beat city rivals Inter 1-0 in a friendly on Saturday before then drawing 0-0 with Real Madrid on Thursday, only to lose 10-9 on penalties.
"The most important thing is not having conceded a goal in both matches," Galliani added. "This has not happened for a long time. Therefore, we can already be satisfied."
Milan kick off their 2015-16 campaign with a tricky trip to the Stadio Artemio Franchi on August 23 to take on Fiorentina.
