The Chilean remains determined to add a centre-half to his squad after recruiting midfielder Fernandinho, winger Jesus Navas and forwards Stevan Jovetic and Alvaro Negredo.
But having spent ┬ú93m so far this summer, Pellegrini admits that City still require further additions before the start of the new season.
“The club has spent money on important players, like Jovetic and Negredo,” Pellegrini said. “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 is not absolutely complete but it’s very near to being complete.
“I don’t speak about rumours. I think today we have the players that we need here.
“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┬áface Newcastle in their opening game of the Premier League season in just over three weeks and Pellegrini admits it is crucial that his team make a strong start to the campaign.
“It is important to make a quick start and to win the first league game because if you lose ground it is difficult to recover,” he said.
“The English Premier League is a different league than 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.”