The 27-year-old midfielder missed Manchester City's last two fixtures against Stoke City and Viktoria Plzen with a thigh injury, but has returned to first-team training ahead of the fixture against the Premier League champions.
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Manchester City are 10/1 with bet365 to beat United 2-0 on Sun
Pellegrini has also revealed that Micah Richards is in contention to make City's matchday squad for the first time this season after recovering from a hamstring problem, while Gael Clichy is a doubt after returning to training on Friday.
"The players who were injured were Micah Richards, he has worked normally with the whole squad, same thing [with] David Silva and [Gael] Clichy starts today," Pellegrini told reporters.
"It's the first day for him [Clichy] so maybe he will not be ready for next Sunday but all the other players expect [Martin] Demichelis are fit, no problems."
Despite managing for the first time in England, Pellegrini insists he understands the significance of the fixture against United and says his side will be aiming to secure three points against the Premier League champions.
"I don't need to be here to know how important the derby is, but working here and living here I know it is a special game.
"It is a match of six points. It is very important to win, [against] one of the most important teams.
"It is more important to win than not to lose. Of course if you cannot win it is better not to lose, but we will try to win from the beginning."