Jurgen Klopp's men have endured a remarkably poor season so far, but a run of three wins on the bounce has seen them climb to 12th, having previously looked in danger of falling to an unthinkable relegation.
And Allegri knows Juve will need to be at the top of their game to come away from the first leg at Juventus Stadium with the advantage.
"Tomorrow we'll need to play with plenty of intensity," he said. "Their four strikers are fast and dangerous.
"Dortmund are a well organised team who play good football, especially in the final third. They score plenty of goals.
"We must keep a clean sheet tomorrow. I believe we have an excellent chance of getting through to the next round.
"Klopp has made great strides in Europe. He's rebuilt Dortmund and is a great coach."
Asked about Dortmund's league position, Allegri said: "It's an anomaly. I think they'll be in and around the top spots come the end of the season."
Goalkeeper Gianluigi Buffon, meanwhile, is optimistic about his side's chances.
"We want to try and keep our Champions League dream alive for as long as possible," he added. "We're up against one of the best teams in Europe. They can beat anyone and we have respect for them.
"We're curious to see how we measure up with Dortmund tomorrow night."
