The 24-year-old Alvarez is scheduled to start for Argentina for the third time at the Olympics on Tuesday in Lyon (16:00 BST) against Ukraine.
Alvarez extended his contract with City for another year in March 2023, bringing his total tenure there until 2028.
When asked about his future with City, Alvarez responded, “There is a lot of talk,” prior to the match against Ukraine.
“Since the Olympics are a brief competition, my attention is concentrated here. I feel great at Manchester City, where I’ve played a lot of minutes.
“However, after the Games, we shall see. I will first try to take a few days off.
Alvarez was a substitute in May’s FA Cup final loss by City to Manchester United, and he has since been connected to a transfer to Atletico Madrid.
“Maybe it’s annoying to be out in big games, players always want to help on the pitch,” he said. “But my season was good, so I’m very happy.”
While on a preseason tour of the United States with City, manager Pep Guardiola acknowledged that Alvarez was contemplating his future.
Guardiola said, “I don’t think about replacing,” exterior
“The other players also want to play during crucial periods, as far as I’m aware.
“Eighteen or nineteen of our guys want to participate in the big games.