City can equal a 103-year-old club record of nine successive top-flight wins if they beat Everton at Goodison Park on Sunday.
Pellegrini's men won their final six Barclays Premier League games last season to put some gloss on a generally frustrating campaign.
They have carried the momentum into the new term with back-to-back 3-0 demolitions of West Brom and champions Chelsea.
Pellegrini did oversee eight successive league wins during the 2013-14 title-winning season but not since 1912, also across two seasons, have City bettered such a sequence.
Equalling it would be a notable achievement - and City could then set a new record against Watford the following week - but Pellegrini is focused only on the bigger picture.
The 61-year-old said: "It matters to have three more points in the table and it is very important to continue in the same way we played the first two games, because we must be a consistent team during the whole season.
"But if that is a new record, that is a thing for me that is not important."
Pellegrini acknowledges the task ahead of his side could also be a tricky one
Everton have also made an unbeaten start and were impressive as they beat Southampton 3-0 last weekend with two goals from Romelu Lukaku.
Prior to Pellegrini's appointment they lost just twice in 12 meetings with City and their statistics remain strong despite four games without a win.
The Merseysiders have lost just one of their last six home league matches against City, who have only won three times in their last 18 trips to Goodison.
Their 1-1 draw in January also put a dent in City's doomed title defence.
Pellegrini said: "It is a difficult challenge
They are always a difficult team, they play very good football.
"In the first game maybe they didn't play very well against Watford but they scored two goals
In the second game they played very well and scored three goals.
"They have Lukaku in a good moment and they have players coming back from a lot of injuries
We must concentrate very much and play with a lot of intensity if we want to win there."
City are unlikely to give a full debut to their new £32million signing Nicolas Otamendi this weekend with Pellegrini set to keep faith with captain Vincent Kompany and Eliaquim Mangala in central defence.
But midfielder Fabian Delph, controversially signed from Aston Villa for £8million in the summer, is in contention to play having overcome his pre-season hamstring injury.
Source : PA
Source: PA