Allegri steered his side past the Spaniards in the quarter-finals of last season's competition but despite that, and Barca's loss of forward Neymar to Paris St Germain for a world record fee, he believes the Catalans remain tough opponents.
Juve visit Ernesto Valverde's Barca in their opening group match on Tuesday and Allegri said it would be "extraordinary" if his team could keep a clean sheet against them for the third time in 2017 following their 3-0 aggregate victory in April.
"I know (Barcelona) well, this will be the twelfth time playing against them," Allegri told a news conference on Monday. "To try again against (Barca forward Lionel) Messi will be a huge stimulus.
"Despite losing Neymar, Barcelona are, along with Real Madrid, the strongest team in the world. To go three games against them without conceding a goal (this year) would be extraordinary.
"I repeat, along with Real Madrid they are favourites to win the Champions League."
Juventus lost last season's Champions League final 4-1 to Real Madrid in Cardiff and Allegri urged his team to start their new European campaign with a bang.
"It's the first game of the Champions League after last year's run and the disappointment of defeat. We have to return and start with great enthusiasm and desire," he said.
"Winning the Champions League can't be an objective, it is a dream."
(Reporting by Rik Sharma; Editing by Ken Ferris)
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