The Serie A giants will play the first leg at San Siro Feb 20 and visit the Nou Camp March 12 in the second-round tie, reports Xinhua.
"We ended up with the strongest team in the world," said Allegri after the draw was announced Thursday.
"We'll still try to get through this round, hoping to be luckier than we were last year."
These sides already clashed last season in both the group stage (drawing 2-2 at the Nou Camp and losing 3-2 at home) and the quarterfinals, where they drew 0-0 at San Siro and Milan lost 3-1 in Spain.
Milan vice president Adriano Galliani is stunned that the Rossoneri are to face Barcelona again.
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"It's incredible, we'll be playing them six times in just over a year," said Galliani.
"Barcelona were assigned to us because the other teams could not face each other, so we were the default option. Barcelona play the best football in the world with the best players in the world. We'll try and last season we made a good impression," he said.