After a disappointing campaign under Massimiliano Allegri and then Clarence Seedorf in 2013-14, the Italian giants have shown signs of improvement with Filippo Inzaghi at the helm.
Saturday's 0-0 draw at title challengers Roma - despite playing the final 20 minutes with 10 men after Pablo Armero was sent off - was another encouraging result, with Milan heading into the mid-season break having lost just three of their 16 Serie A matches this season.
Inzaghi's men lie seventh in the table, just two points from third and the final Champions League qualifying berth.
With the previous season's eighth-placed finish seeing them miss out on European qualification altogether, Galliani sees no reason why the improvements under Inzaghi should not lead to Milan challenging the top three this time around.
"The match in Rome was one in which we showed we were a team: we showed spirit, desire and determination, even with 10 men we continued to fight," he told Corriere della Sera.
"If we play like this we can compete for a Champions League place.
"It seems to me like the tide has turned. Last year we always lost against the big teams."
