"We've made good headway in getting him here and we're going to continue trying hard," Real Madrid sports director Pedja Mijatovic told the club's website on Tuesday.
Mijatovic hailed the abilities of the 32-year-old defender who captained Italy to a fourth World Cup title only days ago.
"If you focus on what he's contributed over the last two years, I would keep him here until he is 40 years old," the former Real player said of the Italian.
"His philosophy, winning attitude, and desire make him a unique defender."
Cannavaro, who joined Juventus from Inter Milan in 2004, also helped the Bianconeri win two back-to-back Serie A titles.
"I can appreciate that Cannavaro was a huge reason why Juve won two Scudetti and why Italy won the World Cup," he added.
The Madrid powerhouse has also been linked with Cannavaro's Juve teammates Emerson and Gianluca Zambrotta in light of the football scandal that could see the Italian champions relegated to Serie C.
Mijatovic, who was appointed be newly-elected Real Madrid president Ramon Calderon earlier this month, did however admit it won't be easy to lure the three players to the Bernabeu.
"It's not that easy," the Serb said. "They have clauses that require paying Juventus, whether they are relegated or not. The good thing is they all want to come to Madrid, making the process a bit easier."
Mijatovic insisted that the club is willing to do whatever it takes to end their three-year streak without a major trophy.
"After three bad years without any titles, we need to build a winning team as soon as possible," Mijatovic said.
"We're planning everything to win a title this year. We cannot make any mistakes."