Atletico are determined not to let their prized asset leave and hope the striker, who has scored over 100 goals for the club, can be convinced to stay once his participation in the Copa America is over.
Atletico are also unwilling to enter into negotiations with other clubs regarding Aguero, who has a buy-out clause of 45 million euros in his contract.
Sporting director Jose Luis Perez Caminero said on Wednesday: "At this moment, Atletico feel Kun Aguero is an asset to our squad and we're not considering him leaving and, therefore, neither are we considering any negotiations for him.
"He's one of the best players we can find and we trust that when the Copa America finishes he will return to Atletico Madrid and be as important a player as he has been in previous seasons."
Regarding the reported interest in Aguero from clubs both home and abroad, Caminero said: "Big teams are always keen on great players and we are fortunate enough to have Kun and at this stage we are not considering anything.
"We are a team who want to have the best players and Kun is one of those. What we want is that the lad finishes the Copa America, comes here and continues to show what a great player he is and helps make this team better."
He added on his club's official website: "He (Aguero) has to realise that the club don't want to lose him, that everyone here hopes he stays and that if we manage to change his mind it would make us all happy.
"There are few players like him in the world and Atletico Madrid have this player. The only thing that we're thinking about is Kun continuing to wear the Rojiblanco shirt next season.
"When he comes we will try to help him stay, because the important thing is that a decision is taken for the good of the club and the player, who knows that he has a buy-out clause of 45 million euros."