Stones claim that the Argentine striker has an impeccable scoring record, but gets overlooked for awards because of his low-key profile.
Aguero scored a hat-trick in the midweek Champions League win over Borussia Monchengladbach and has now scored nine goals in five games for City this season.
Stones said: "He's one of those players who comes in, gets on with his work and with his own life.
"The awards will come to him. There are a lot of top players out there and he's definitely up there.
"If he keeps playing like he is then I'm sure there's no reason why he can't be nominated and going for these.
"His goalscoring record is a joke. It's not just that - his link-up play, movement, these things go unrecognised because of his goalscoring but he's an all-round player for his size.
"He can head a ball. He's the full package and it's great for me to play alongside him day in, day out."
Overall, the 28-year-old has netted a remarkable 145 goals in 213 appearances in all competitions for City since joining from Atletico Madrid in 2011.