Antonio Conte's men managed just two points from their opening three games and, with second-placed Galatasaray facing rock-bottom Copenhagen, a home defeat to Real could leave them five points adrift of a qualification spot for the last 16.
But Conte, who saw his side lose 2-1 at the Bernabeu, believes the home fans can make the difference.
"I hope the Juventus Stadium is going to be a boiling cauldron on Tuesday night, so that the fans can push us to victory," he told Juventus TV.
"We have already shown in Madrid what we can do.
"Madrid have been constructed to win their 10th European Cup, but we must not be afraid."
Juve were boosted on Saturday by the return from injury of influential forward Fabio Quagliarella, who played the last 15 minutes of the 1-0 win at Parma.
They will be without defender Giorgio Chiellini, though, after he was sent off in the reverse fixture last month.
The Serie A champions have lost just once in the league - a 4-2 defeat at Fiorentina, where they had led by two at the break - and have leaders Roma in their sights.
But at a club that has twice been crowned European champions, the demand to do well in continental competition is high.
Victory against a Real side that has reached the semi-finals in each of the last three seasons would signal Juve's intent, but Carlo Ancelotti's charges represent a substantial challenge to overcome.
The 3-2 win over Rayo Vallecano on Saturday, in which Cristiano Ronaldo scored twice to take his season's tally to 22 in all competitions, came on the heels of a 7-3 triumph over Sevilla, underlining the visitors' goalscoring threat.
Ronaldo scored both goals in the meeting between the two sides in Spain, moving him into third in the competition's all-time scorers list.
The Portuguese is six shy of Barcelona's Lionel Messi and 15 short of overhauling Real legend Raul, who has 71.
Ancelotti's side will secure their place in the knockout stages with a victory.
