Pep Guardiola has often been without an out-and-out striker this term with Gabriel Jesus also sidelined.
City will now go all out for a replacement for Aguero and Erling Haaland will be top of their wishlist.
That spells bad news for cross-town rivals United, who were hoping to strike a deal for the Borussia Dortmund star themselves.
Haaland has a £67million release clause that becomes active in 2022 but United were hoping to push through a transfer this summer because Barcelona and Real Madrid are unlikely to have the funds until next year.
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City owner Khaldoon Al Mubarak said: “Sergio’s contribution to Manchester City over the last 10 years cannot be overstated.
“His legend will be indelibly etched into the memories of everyone who loves the club and maybe even in those who simply love football.
“This is not yet the moment for farewell words and speeches. There is still much to achieve in the remainder of the time we have with Sergio, and we look forward to his contributions to the challenges which lay ahead.
“And we look forward to the opportunity to bid Sergio a fitting farewell at the end of the season.”