City have been among the most active Premier League clubs in the transfer market this summer after missing out on the title last season and losing to Wigan Athletic in the FA Cup Final.
Fernandinho, Jesus Navas, Alvaro Negredo and Stevan Jovetic have all been signed by City since Pellegrini replaced Roberto Mancini as coach at the Etihad Stadium.
However, despite having already spent over £80million on new signings, Pellegrini is not ruling out further additions before the transfer window closes.
"The club has spent money on important players, like Stevan and Negredo," said Pellegrini.
"But we must remind you that last year there was Balotelli and Tevez, so we had to replace two very good players with another two very good players.
"So, we have the month of July and some days of August to finish the squad completely. It's not absolutely complete, but it's very near to being complete."
Pellegrini has been linked with a £20million offer for Pepe, but the City boss does not want to talk about specific transfer targets.
He added at a press conference in Hong Kong where City are competing in the Barclays Asia Trophy: "I don't speak about rumors. I think today we have the players we need here.
"I just said that we will see what happens in this month and during August.
"I'm not talking about specific names because it's not better for us, so I don't talk about Pepe or any other names."