Atletico's majority-shareholder Miguel Angel Gil told Reuters that offers from Spurs for Aguero and strike-partner Diego Forlan, and one from Chelsea for Aguero had been turned down.
The 22-year-old Aguero, who joined Atletico from Independiente in 2006, agreed a two-year extension to his deal.
"The club have always treated me well and for this reason I wanted to renew," Aguero told a news conference at the Calderon.
"I'm settled and happy to continue here, and I hope to stay for many years."
The agreement saw the player's buy-out clause reduced from 60 to 45 million euros, which has increased media speculation of a possible exit in the near future.
"The day I want to leave it will be my decision," Aguero added. "If in June we decide, the club and I, that a change is best it will be a decision taken by everyone."
Europa League champions Atletico are out of Europe and the King's Cup and 10 points adrift of the Champions League qualification places in La Liga after a 2-0 home reverse against Athletic Bilbao on Sunday.
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