City have already had a busy summer, signing four new players for a combined cost of £90million as well as appointing Pellegrini.
Pellegrini, speaking at a press conference in Hong Kong, told reporters: "The club has spent money on important players, like Stevan and Negredo.
"But we must remind you that last year here there was (Mario) Balotelli and (Carlos) Tevez, so we had to replace two very good players with another two very good players.
"So, we have the whole month of July and some days of August to finish completely the squad. It's not absolutely complete but it's very near to being complete."
City continue to be linked with other targets, including Real Madrid and Portugal defender Pepe.
City have lost one senior centre-back this summer following Kolo Toure's free transfer to Liverpool.
Pellegrini said: "I don't speak about rumours. I think today we have the players that we need here.
"I just said that we will see what happens in this month and during August. But 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."