The Italy captain, whose contract at Real runs out at the end of the season, wanted to end his career at hometown club Napoli until president Aurelio De Laurentiis said he would not sign the 35-year-old because he was too old.
"Juve's offer is the biggest and most interesting," agent Gaetano Fedele told Italian media, adding Cannavaro was also a target in England, Russia and Germany.
"There's every chance this will be the decisive week."
Real are unlikely to offer him a new deal while Juve have not made any comment.
Media reports said talks had included the option of him becoming a Juve director once he retires.
The 2006 world player of the year wants to captain holders Italy in the 2010 World Cup having missed Euro 2008 through injury.
Juve fans were angered when Cannavaro joined Real in 2006, the year they were demoted to Serie B in a match-fixing scandal.
Other top players such as Alessandro Del Piero and goalkeeper Gianluigi Buffon stayed and won immediate promotion.
After media reports on Sunday said the Turin club were in talks with Cannavaro, some supporters expressed their displeasure on internet message boards.
