The Argentine striker signed a one-year contract extension back in May, but was subsequently linked with a move to Real Madrid.
However, the former Atletico Madrid forward is happy at the Etihad Stadium and did not consider leaving the Premier League club.
"One or two offers might have been around but I was not interested in them," Aguero told the Sun Sunday.
"The thing was to stay where I was enjoying my football.
"I am very happy with Manchester City. I love Manchester. I have signed for another year. I'm happy to be here as I've been treated so well."
Aguero memorably scored the winner against Queens Park Rangers in May 2012 which secured City a first top-flight title in over 40 years.
But last season's failure to win any trophies prompted City to replace Roberto Mancini with Manuel Pellegrini as manager, and Aguero is hoping for a positive campaign.
He added: "Yes, we want all four [trophies]. Champions League, Premier League, Capital One Cup, FA Cup. Let's hope so.
"In 2011/12 it was great to win the title in my first year. Last season was not so good. We disappointed. We got to an FA Cup final but that was no use because we could not carry off the trophy.
"We are trying to put into practice what Manuel wants tactically. We respect what he is asking us to do.
"Sure, we are playing in a different style, but with the advent of all the new signings, it bodes well for the season. Let's hope we can keep going."