Gazzetta dello Sport says Benitez met with his agent Manuel Garcia Quillon at Liverpool's training camp in Madrid last week.
Juventus and Quillon have apparently ironed out a contract worth 4.5m a year.
They also managed to get Benitez to accept to reduce his staff from 12 to six personnel.
However, the conclusion of any deal depends on Liverpool's new President Martin Broughton who is currently trying to find a buyer for the club.
Juve want Benitez to negotiate a release from his contract at Liverpool as they're not interested in paying compensation for the Spaniard.