The Spanish side named former Juve boss Fabio Capello as their new coach last week and now hope to raid the Italian champions for 32-year-old Cannavaro.
Real sports director Pedja Mijatovic told the club's website: "We've made good headway in getting him here and we're going to continue trying hard.
"I'm sure there will be some news in the next few days."
Real are looking to rebuild after three years without a trophy, and Mijatovic believes Cannavaro could provide the winning touch.
"I can appreciate that Cannavaro was a huge reason why Juve won two Scudetti and why Italy won the World Cup," said Mijatovic.
Juventus, who appointed 1998 World Cup winner Didier Deschamps as their new coach on Monday, are currently embroiled in a match-fixing trial and face the threat of relegation from Serie A.
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Looks like first of many.