Less than 48 hours after clinching their fourth successive Serie A crown, Juve are re-focusing their efforts on Europe, where they are hoping to reach their first Champions League final since 2003.
Standing between them and a place in the showpiece, though, are Spanish giants Real, who were crowned European champions for a record 10th time last season.
It is a tough test for Juve, who are still in the running for the treble this season, but Pirlo is in optimistic mood ahead of Tuesday’s first leg in Turin.
“We have the same chances as they do to progress,” Pirlo said on his club’s official website.
“We weren’t ready for the Champions League in previous years. But this team has gained experience and we know we can do well and play without fear.
“Now that we are here, we want to go all the way.
“To win it would be a dream come true, for me and for my team-mates.”
Pirlo, who has played in seven European semi-finals and won the Champions League title twice at AC Milan under current Real coach Carlo Ancelotti, knows the Spaniards must be respected, though.
The 35-year-old added: “Real are the most important club in the world.
“They have a lot of experience in this type of game and have a team of champions.”
Juve are unbeaten at home in European competition this season and have won five and lost just one of their seven meetings with Real in Turin.
The previous time the two superpowers met in Italy was in last season’s group stage, with the game ending 2-2.
“The first leg is crucial and we’ll need to play with intelligence as we have done in recent years,” Pirlo said. “We’ll be mindful but also show some swagger, because we have a dream to fulfil and nothing to lose, but also aware that there’s a second leg to follow.”
The hosts will be without midfielder Paul Pogba, who has been sidelined since March with a hamstring injury.
Real go into the contest without the services of midfielder Luka Modric and striker Karim Benzema because of injuries as they look to end a run of seven successive trips to Italy without a win.
However, Ancelotti does have Gareth Bale back, with the Wales international coming on as a second-half substitute in Saturday’s 3-2 triumph at Sevilla after recovering from a calf injury sustained in the Champions League quarter-final clash against Atletico Madrid.
Real, who are two points behind leaders Barcelona in La Liga with three games remaining, are confident they can bring home a positive result against one of Ancelotti’s former clubs on Tuesday night.
Ancelotti was in charge of Juve from 1999 until 2001 before joining Milan.
“We have an Italian coach that knows Juventus very well,” Real midfielder Toni Kroos said. “I think that will help us.
“We are going to do all that we can to reach the final knowing that no club has managed to defend the Champion League crown.
“This is our biggest challenge of the year.”