It has been suggested that Mancini is working on borrowed time, with the City board ready to move in a different direction.
Premier League title success last season earned Mancini plenty of plaudits, but he has overseen group stage exits in the UEFA Champions League in each of the last two seasons and is struggling to mount a successful defence of City's domestic crown.
Ending the season empty-handed could see him ushered through the exits and a new man drafted in.
Jose Mourinho is expected to become available in the summer, with question marks hanging over his future at Real Madrid, and City would be among those in the market for his services.
Aguero, though, feels City should be seeking stability, with Mancini retaining the full backing of those in the playing squad at the Etihad Stadium.
The Argentine forward said: "Roberto is a very hard-working coach who has won important trophies that should be valued by everyone.
"I have a good personal relationship with him, too. He talks to me a lot in training, tells me what kind of movements I should make."
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