Aguero has suffered another injury playing for Argentina this time to his thigh.
And even if the star striker manages to play again at the WorldCup,City are concerned about the number of muscle injuries he picks up.
Aguero, 26, will be examined by specialists when he returns from Brazil.
City believe their hitman may need an extended break to help cure his problems, having been plagued by hamstring and muscle injuries last season.
Aguero missed 15 games during City’s title-winning campaign but still managed to notch 17 goals in just 23 league appearances.
The Premier League champions, meanwhile, have allowed Brazil-born Marcos Lopes, 18, to join Lille on loan for next season.
The Etihad outfit want the attacking midfielder to have more first-team action in a bid to accelerate his development.