The Milan chief is hoping for a repeat of last season's 2-0 Champions League last-16 victory when the Rossoneri host the Catalans for the fourth time in two years
The two sides were pitted against each other in the group stages in 2011 before meeting in the quarter-finals later in the same campaign, and then met in the first knockout stage in 2012-13 where Milan recorded a 2-0 victory at San Siro before losing the second leg 4-0.
And after being drawn alongside each other in Group H this season, Galliani believes otherworldly forces are at play.
"We are facing them at home for the fourth time in 24 months," he told reporters. "Destiny wanted it like this; we were not able to fight it.
"The first in the world will play against the top Italian team in Europe, according to the [Uefa] rankings. Certainly, another 2-0 win would be a dream."
Galliaini also believes Barcelona pose a unique threat in world football, given the attacking talents of two South American superstars.
"Nobody else has a pairing like Messi and Neymar," he added.