Allegri, who was given the boot by Juve shortly after his uncharacteristic outburst to match officials, had been on the sidelines for an entire season.
He signed a two-year deal, worth €5 million (US$5.7m) a season, to return to the San Siro having last coached Milan 11 years ago.
Allegri scooped a dozen trophies during his two stints with Juventus, including five consecutive league titles from 2015 to 2019.
Now he is poised to lure three of his former charges to his new club, with defensive duo Andrea Cambiaso and Federico Gatti on his radar as well as striker Dusan Vlahovic.
Cambiaso has admirers
Cambiaso, who came close to making a January switch to Manchester City, is being monitored by Milan as a replacement for Theo Hernandez but would cost around €60m (US$68.5m).
Left-back Hernandez, who has one year remaining on his contract, has rejected the lucrative advances of Saudi Pro League outfit Al-Hilal that are now managed by former Inter Milan boss Simone Inzaghi. Atletico Madrid has stepped up their interest.
Cambiaso's ability to also play at right-back is appealing. The 25-year-old could fill the position vacated by Kyle Walker, who returned to Manchester City following an unimpressive loan at the San Siro.
Gatti shows uncertainty
Gatti was close to signing a contract extension when Thiago Motta was head coach, but their professional relationship was rocky.
Under interim manager Igor Tudor he was set to extend his contract with Juventus until June 2030, with negotiations reportedly in the Italian media that he would virtually double his annual salary from his current wage of €1.5m (US$1.7m).
Yet once talks started to stall, Juventus contemplated selling the 26-year-old center-back with Premier League sides Aston Villa, Newcastle United and Nottingham Forest closely monitoring his situation at the Turin titans.
Inter Milan and Napoli also showed interest, although now Allegri has landed a Serie A gig then Milan is a viable destination for a player who has rapidly risen through the ranks in Italy.
Vladovic's salary dilemma
Vlahovic’s talks with Juventus about a contract extension recently broke down, as the club wanted to reduce his current annual salary from €12m (US$13.7m). The Serbia hot-shot has one season left on his deal with the Bianconeri, who are keen to cash in before he becomes a free agent.
Although Allegri is pushing to sign Vlahovic on a five-year contract, Milan are only offering an annual salary of €7m (US$8m) and buying him for €30m (US$34.2m).
Vlahovic turned down lucrative offers in January to move to either the Saudi Pro League or Turkish Super Lig, as he was holding out for a Premier League move.
Fenerbahce have returned for Vlahovic during the special transfer window. According to Fanatik, the club would be prepared to pay Juventus the same fee as Milan, but can offer the 25-year-old an annual wage of €10m (US$11.4m).
Atletico Madrid have also shown serious interest in Vlahovic, but the Spanish giants would only consider including a player in any deal.
Allegri is keen to strengthen his squad, ideally with players he has previously coached. Having won the 2010/11 Scudetto at Milan, he is bidding to secure another Serie A title next season.