The Italian stopper is hopeful that the Rossoneri can eliminate Barca and progress in the Champions League, while urging Juve to focus on their own Serie A title race
Milan host the Catalan giants on Wednesday in the first leg, and with the Rossoneri being the only Italian club left in Europe, Chiellini is hoping that they will be able to progress in the competition.
"Every fan will be watching the match on Wednesday," Chiellini is quoted as saying by ANSA.
"For us Italians, it would be good that Milan could go as far as possible, especially at a moment when the deficit in the Uefa club ranking is so big."
The 27-year-old then urged Juventus not to obsess with Milan's results in the Serie A title race despite the Bianconeri sitting four points adrift with nine matches left to play.
"We have to think about winning our games, which will not be easy," Chiellini added.
"The rest will depend on what Milan do, because if they continue like this, they will win."
The Rossoneri will visit Catania on Saturday in Serie A while Juventus host Napoli on Sunday.