The 51-year-old's five-year reign with Juventus ended last month.
"I'm going to take a year off to recharge the batteries and take my personal life back in hand," Allegri said in Milan.
"The last 16 years have felt like being in a spin-dryer. You let things go a bit with family, children and friends.
"I'll use this year to recharge my batteries ahead of the next season."
Juventus won an eighth consecutive Serie A title in April, which was Allegri's fifth in as many years.
He also lifted the Coppa Italia on four occasions since replacing Antonio Conte in 2014, and reached two Champions League finals.
Allegri also led AC Milan to their last Serie A title in 2011 and had been linked with a return to the San Siro, as well as a move to the Premier League.