City have already had a busy summer, signing four new players for a combined cost of £90million as well as appointing Pellegrini.
Deals for Fernandinho and Jesus Navas were completed before Pellegrini's arrival with moves for forwards Stevan Jovetic and Alvaro Negredo finalised last week.
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."
City are preparing to face Premier League rivals Sunderland in the final of ther Barclays Asia Trophy having beaten South China 1-0 in their opening match of the tournament.
Pellegrini is pleased with City's pre-season work so far, having begun with a trip to South Africa earlier in the month.
They move on to play a tournament in Munich next week.
The Chilean said: "It's important to make a quick start and to win the first league game because if you lose ground it is difficult to recover.
"The English Premier League is a different league than what I have worked with before, but I am not concerned about that.
"Of course it is always good to have more time, but I hope the team will be prepared."
The only frustration so far for City has been poor weather in Hong Kong, with torrential downpours making training difficult and even leading to rumours the final matches could be cancelled.
Pellegrini said: "The conditions are difficult, but the players are working very hard.
"It is not exactly what we wanted, but we have been able to work in training and we must be optimistic."