City began their campaign with a comfortable 3-0 win at West Bromwich Albion on Monday and three points against Chelsea, who drew 2-2 with Swansea City on Saturday, would give Pellegrini's men a five-point advantage over the champions.
"We are not thinking about the title in the second game but we are thinking about trying to win our points here at home, especially playing against the champions and the best team from last season," Pellegrini told a news conference on Friday.
"Especially also against one of the teams that has a lot of chances to win the title like Arsenal, Manchester United, Liverpool and Tottenham Hotspur, so to try to win the three points here at home is very important for our team."
Midfield powerhouse Yaya Toure, a dominant force in City's two Premier League title-winning sides in 2012 and 2014, failed to make the same impact at the Etihad last season.
However, the Ivorian was back to his imperious best against West Brom, scoring City's second goal from the edge of the box, and Pellegrini believes Toure will play an integral part in the club's bid to regain the title.
"Every player has good and bad games. I hope he can continue from Monday because he played very well," the Chilean said.
"Yaya last season, as every player, had good games and bad games. He's done very well this season.
"All of us hope that he will continue because he has done very well."
Midfielders Fabian Delph and Fernando are ruled out against Chelsea with injury but striker Aguero could be in contention as the Argentine continues to regain fitness after missing most of the pre-season due to his involvement in the Copa America.
Fellow strikers Edin Dzeko and Stevan Jovetic have left City during the transfer window but Pellegrini said he was happy with his forward options.
"For the moment we have here (Wilfried) Bony, (Sergio) Aguero, (Raheem) Sterling and Kelechi (Iheanacho)," he said.
"I think the fourth striker must be a young player and in this case it is Kelechi.
"We have a good squad at this moment but if we can improve it in a couple of positions it is better."
(Reporting By Michael Hann; Editing by Clare Fallon)
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