Allegri: Barca favourites to win Champions League
The Bianconeri have not lifted the trophy since the 1995-96 campaign, despite finishing as runners up under Allegri in 2014-15 and 2016-17, but the arrival of Cristiano Ronaldo has seen many tip them for Champions League glory this term.
Despite losing at home to Manchester United in Europe last time out, Allegri is aiming to sustain a challenge on multiple fronts - with Juve now eight points clear at the top of Serie A - but he is not getting carried away yet.
"There are still many games to go in Serie A and we have a lot of difficult games to play until the end of the year, against Roma, Inter, Atalanta, Fiorentina and Sampdoria," he said.
"But in the Champions League, we have to take it one step at a time. We want to qualify for the last 16 and in first place.
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"Barcelona are the favourites to win the competition, in my opinion. Then there are teams, including us, with the ambition to win it. We have that same desire every year.
"Last year, I said that the favourites were Real Madrid. This year, I think it's Barcelona. I hope to be wrong this year."
Both Real Madrid and Bayern Munich, regular contenders in this competition, have endured difficult starts to their domestic league campaigns, but Allegri is reluctant to write them off in Europe.
"The Champions League is different," he said. "In a period when Real Madrid were much worse - they were 15 points behind Barcelona - they still have the opportunity to go through to the next round. [Their form] counts for nothing."