The Mexican has been impressive with the Dutch team since arriving in July 2019.
He is now a key part of the first team, and the 23-year-old wants to go to greater heights.
He dreams of a move to City and the Premier League one day. Alvarez has no goals and assists in six appearances this term, but he has been an assured presence in defensive midfield for Ajax.
Asked about his future by reporters, he told Voetbalzone: "I would really like to achieve [an Eredivisie title] one day and then it is a dream of mine to play in the Premier League one day.
"Manchester City is my favourite club, so that would be perfect."