The 28-year-old has not featured in the Professional Football Association (PFA) Team of the Year and has never won the PFA Player of the Year award either, something Stones blamed on the Argentine's low-profile lifestyle.
"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," Stones told British media.
"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."
Aguero has scored 105 goals in 153 Premier League appearances, also racking up 26 assists since joining from Atletico Madrid in 2011.
"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," Stones said.
"He can head a ball. He's the full package and it's great for me to play alongside him day in, day out."
Stones was also braced for an encounter with Lionel Messi in next month's Champions League group match against Barcelona.
"You've got to be on your toes and I think the players bring the best out of you," Stones added.
"You have to raise your game and try and compete with the best. That's why you come and play on these big stages to play against the best and try to prove yourself."
(Reporting by Ian Rodricks in Bengaluru; editing by Amlan Chakraborty)
