Galliani believes that for the Rossoneri to win the second leg of their last-16 tie at Camp Nou, the Argentine forward will need to "take a break".
"Messi is a monster, he scores with amazing continuity," he told reporters. "Hopefully tomorrow he will take a break. We are facing the best team in the world.
"I expect a very warm atmosphere, with 100,000 people at Camp Nou. It will be difficult, because we are up against the best in the world."
Milan won the first leg 2-0 at the San Siro last month.