The deal includes an initial payment of £64.4 million (€75 million) and an additional £17.1 million (€20 million) in potential add-ons. This would set a new record sale for City, surpassing the £50 million Chelsea paid for Raheem Sterling in 2022.
Alvarez mentioned he would decide on his future after Argentina participates in the 2024 Olympics, which ended last Friday with a loss to hosts France.
City manager Pep Guardiola had expressed his desire to keep the 24-year-old, stating earlier in August that he "counted" on Alvarez for the upcoming season. "I count on him, but he said in the news that decisions will be made all together," Guardiola remarked.
However, similar to past cases with Ilkay Gundogan, Riyad Mahrez, and Aymeric Laporte, City is not inclined to hold back a player who wishes to leave.
Atletico Madrid, who have also secured a deal to sign Chelsea midfielder Conor Gallagher, has yet to finalize personal terms with Alvarez.
The Argentine striker, who joined City in 2022 for £14.1 million from River Plate, has scored 36 goals in 106 appearances under Guardiola. Alvarez had an impressive first season at the Etihad, winning the Treble, and played a key role in Argentina's 2022 World Cup victory in Qatar.