Spalletti has a deal with Juve to the end of the season and has guided the Bianconeri to fifth place on the Serie A table, four points behind leaders Inter Milan.
Mauro insists Juve should hand Spalletti a new, long-term contract so he and management can open up a new 'cycle'.
He told La Gazzetta dello Sport: "Juve must begin a new era with Spalletti, and I'd renew his contract immediately. We're not just discovering Luciano today; he's a coach who's achieved results everywhere.
"He's only worked poorly with Italy, but he doesn't coach for the national team. And Spalletti needs to work on the pitch. He sees things others don't.
"In Pisa, he changed the game by substituting (Manuel) Locatelli, a substitution few would have made at that point in the game."
On Juve's Scudetto chances, Mauro also said: "The next four matchdays will be crucial for measuring Juventus. The Bianconeri can historically struggle against provincial teams, but then win, like in Pisa.
"If Spalletti has a clean sweep against Lecce, Sassuolo, Cremonese, and Cagliari, well, then new scenarios could open up: it depends on how many points he snatches from his rivals."