Negredo has made a good impression since his £20million summer arrival from Sevilla, scoring off the bench in the last two games against Cardiff and Hull.
The Spaniard also found the net on his debut against Newcastle, only to have his effort ruled out in a tight offside call.
After also scoring on international duty last week, the 28-year-old is pressing for his first City start as Pellegrini's men travel to Stoke in the Barclays Premier League this weekend.
Pellegrini, who briefly worked with Negredo during his short spell in charge of Real Madrid four years ago, said: "I think that in every game he played he did very well.
"He has scored in all the matches so I hope we will see the best of Negredo, that I saw in Spain for the last seven, eight years.
"He was a very young player when I was at Real Madrid.
"He started there and after that, every year, he has been a very important striker in Spain. He will be here in England also."
Negredo is competing with Sergio Aguero, Edin Dzeko and another summer arrival in Stevan Jovetic for a place up front.
Between them the four players cost City £107million and Pellegrini has no firm idea of which pairings might be the most effective.
"No, I don't know exactly," he said. "We have four important players for that combination."
Dzeko has so far been the preferred option alongside Aguero, while Jovetic is still awaiting his debut.
Negredo's performances could put him in line to replace Dzeko but Pellegrini wants both players in good form with a tough spell of fixtures ahead.
Pellegrini said: "Alvaro Negredo is always a very important option, Edin Dzeko is exactly the same.
"They are different players but they are both very good players, so the important thing is how useful both are for the team.
"They have competition always for a place but they can play together also, so they are two important players for the team.
"We have to play seven games in 21 days, so the most important thing is not the 11 that start, but the performance of each player in every game.
"All the players we have, if they give a high performance, have the option to play."
The paths of Pellegrini and Negredo briefly crossed at Real Madrid after the club, having sold the player to Almeria two years previously, exercised a buy-back option on him in 2009.
But with other forwards competing for places in the Real side, notably Cristiano Ronaldo, Karim Benzema and Gonzalo Higuain, he was sold soon afterwards to Sevilla, for a nine million euro (£7.5million) profit.
Pellegrini said: "He had just played that year in Almeria and he had a very good year but in Real Madrid at that moment was Cristiano Ronaldo, Benzema, Higuain, Ruud van Nistelrooy - too much.
"So it was very important for him to continue growing as a player and he signed for Sevilla and it was a very important four years for him."