City are set to pay £46 million (A$96 million) for the 26-year-old Reijnders, who has agreed a five-year contract to move to the Premier League.
The formalities of the deal are still to be completed but it appears City have landed their first major summer signing.
Reijnders was a bright spark in a disappointing season for Milan, who finished eighth in Serie A, missing out on qualification for Europe.
Reijnders, who joined the Italian giants from AZ Alkmaar in 2023, scored 15 goals in 2024-25 and will bolster Pep Guardiola's midfield options following the departure of Kevin De Bruyne.
City will play their first match of the Club World Cup against Morocco's Wydad AC on June 18 and the arrival of Reijnders could have big implications for Grealish's future.
The England international looks set to miss out on City's final 35-man squad for the Club World Cup in the United States.
Last month, the 29-year-old was left on the bench in the FA Cup final defeat to Crystal Palace, and omitted from the squad for the final league game of the season at Fulham altogether.
Grealish, a record signing from Aston Villa four years ago, has fallen down the pecking order since playing a starring role in the 2023 treble-winning campaign and made just seven Premier League starts in 2024-25.
Another midfielder who will not feature in the US is Mateo Kovacic, who has been ruled out following Achilles surgery.
The other English Premier League side heading to the United States for the Club World Cup have also bolstered their squad.
Chelsea have signed striker Liam Delap, 22, from relegated Ipswich Town after triggering his £30 million (A$62.6 milllion) release clause.
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