Mancini is believed to be on the verge of making an offer for Sergio Aguero, as the Atletico Madrid front-man is seen as the perfect replacement for his Argentina strike partner. However, the City boss has indicated that he would be willing to bring in Aguero even if Tevez remains at Eastlands.
"I think it is really difficult to buy any players because all the good teams want these players,'' Mancini said on Sky Sports News.
"But I hope that before the game against [Manchester] United [in the Community Shield on August 7] we can have all these players.
"We have two, three targets but it depends. We need to improve because we are at the moment a few players [short] for competition and we need to have other players.''
For the time being at least, Mancini still has Tevez and the manager is adamant he is still welcome at the club.
"At the moment Carlos is still a City player, like yesterday, like three days ago,'' he said.
"In the future we will see what can happen. But for us Carlos is an important player.
"Carlos wants to leave, wants to come back to Argentina or maybe another country for his family. It is only because of this I think that the club accept to sell Carlos, because I think that we respect his reasons."
Tevez, on holiday after Argentina were knocked out of the Copa America, is said not to be "overly worried" by the collapse of his move to Corinthians.