The 31-year-old, capped 80 times by Italy, spent seven years at Juventus before joining Milan for one season.
The move is set to be part of a deal that will take Argentina forward Gonzalo Higuain in the opposite direction from Juve to Milan.
Higuain will also undergo a medical on Thursday, Milan said on Twitter.
Serie A
Bonucci nets double as Juventus edge out Venezia
01/05/2022 AT 10:08
Bonucci's return to Juve would reunite him with Andrea Barzagli and Giorgio Chiellini, who together formed the so-called 'BBC' defence, which proved to be one of Europe's most formidable rearguards.
World Cup Qualification UEFA
'Italians have no memory' - Euro success will be forgotten if Azzurri miss World Cup - Inside Europe
22/03/2022 AT 14:46
UEFA Nations League
Classy Spain end 10-man Italy’s record run to progress to Nations League final
06/10/2021 AT 17:49