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.
"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.
"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."
Despite their stumble against Manchester United last Champions League matchday, Juventus can clinch a spot in the knockout stages with a result against Valencia.
With that in mind, Allegri is demanding his side not repeat their mistakes from the defeat against the Red Devils, and wants improvement from the whole team.
“Tomorrow we must not fall asleep like we did in the last five minutes against Manchester United. I expect from Dybala to play a good game. Just as I expect a good game to be played by the whole team. We still have to improve.