The striker missed City's victory over Stoke on March 12 due to problems with his knee and it could impact his appearance for the Argentina national team.
Jorge Sampaoli's side take on Italy on Friday before travelling to Madrid next week to face Spain which doesn't allow much time for Aguero to recover and work up his match fitness, despite being with the squad since they met up in Manchester a few days ago.
Sampaoli revealed to reporters that he is unsure if his in-form striker will feature: "We talked to City's doctors about Aguero. We've evaluated the situation. He'll probably sit out the first game".
"If there is a substantial improvement he could travel to Madrid to play against Spain, but I see it difficult because of the little time left".
It will be a big miss for Argentina given his form under Pep Guardiola at City this season, scoring 30 goals in 37 appearances.