Brown says he has always been a fan of the Italian midfield maestro, having first gone up against him when Gordon Strachan's Celtic faced AC Milan in 2007.
He is looking forward to their latest duel on Tuesday night and thinks it is vital for Celtic to keep the 33-year-old quiet in both legs if they are to progress to the quarter-finals.
"Whenever I have played against Pirlo, it has been hard," said Brown. "Maybe he is getting older now and we can catch him. We need to stop him from playing. He has fantastic ability on the ball. He is one of the greats.
"It was my first Champions League game when I played against him when he was with AC Milan. I played against him after that as well, for Scotland against Italy.
"He is a very gifted player, one of the best ever. He still ran the Euros for Italy last year. He has maybe lost his legs a little bit but he still has all the ability and vision with the ball at his feet to make those passes."
Celtic have done their research on Juve since being pitted against them in the draw for the last 16, and Brown recognises that if the Serie A champions are given time on the ball they can be deadly.
"We have watched a lot of DVDs about Juventus recently and he is certainly the one who seems to make them tick," said Brown.
"He seems to get on the ball a lot and passes long and short. He also has the ability to beat a man, while his free-kicks and shooting are really good as well.
"I think if we can put a guy on him to stop him from playing it will help us a lot. Would I enjoy going up directly against him? Of course I would. It would be great but I will have to see if I am in the team."
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