Silva in fight to face United
The Spain midfielder has missed City's last two games after suffering a thigh injury while on international duty.
Defender Micah Richards could also come back into contention after missing the start of the season with hamstring trouble but the Etihad Stadium clash is likely to be too soon for left-back Gael Clichy.
Pellegrini said: "Richards is working normally with the whole squad, same thing for David Silva and Clichy starts now.
"Maybe he will not be ready for next Sunday but all the other players, except (Martin) Demichelis, are fit, no problems."
City will be led by Vincent Kompany after their inspirational captain made a successful return from injury in the midweek Champions League win at Viktoria Plzen.
Kompany had missed the previous three Barclays Premier League games after suffering a groin injury in the season-opening win over Newcastle.
The Belgian brought strength and shape back to the defence after unconvincing displays in his absence.
Pellegrini said: "I think Vincent is a very important player for us.
"We worked well without Kompany. If you see our numbers in games he didn't play, we had three clean sheets, but he is always important. He gives confidence to the whole team."
Pellegrini knows facing the champions is a crucial early test for his side.
City began the season as joint favourites for the Premier League crown but have not impressed on the domestic front since the 4-0 thrashing of Newcastle.
They laboured in a goalless draw at Stoke last week but, buoyed by an impressive display against Czech champions Plzen, Pellegrini is targeting victory against United.
He said: "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.
"Manchester United will always be one of the teams trying to win the Champions League, so playing at home against Manchester United is very important.
"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."
City put aside their recent lethargy to win 3-0 in Plzen with goals from Edin Dzeko, Yaya Toure and Sergio Aguero.
After failures in Europe in the past two seasons, it was a performance that lifted the club at a timely moment in a critical week.
Pellegrini said: "For us it was very important to start the Champions League winning and to have three points playing away.
"Of course that gives confidence to the players."
Pellegrini believes his side will now continue to improve as the players grow used to his style.
He said: "It was a good start, not as good as we wanted, but normally it is very difficult to start in a better way.
"We know we must improve every game. It is very difficult to change styles to have new ideas.
"Until December it is very important to win and with winning it is easier to improve. But we have to improve a lot of things."
United are also finding their feet under a new manager after David Moyes took over from Sir Alex Ferguson in the summer.
Sunday's clash will be the first Manchester derby since 1986 not to feature Ferguson in the United dugout.
Pellegrini said: "It is impossible not to be under a lot of pressure - not in replacing Alex Ferguson but managing Manchester United, or big teams.
"You are always under big pressure but that is a good way to work because you know what you have to do."
Moyes boasts a good record against City with his old Everton side having beaten them in 12 out of 22 meetings during his 11-year tenure at Goodison Park, including six of the last eight.
Yet Pellegrini has overcome Moyes before, beating the Toffees with Villarreal in a Champions League qualifier in 2005.
The Chilean said: "I know he had good results against Manchester City when he managed Everton.
"I had also had a good record against Everton when he was their manager."
United are yet to hit their stride this season but Pellegrini is not reading much into their form.
He said: "It's not my duty to analyse how they start. It is a very good team and David Moyes is a very good manager.
"I think they have a lot of great players, (Wayne) Rooney of course is one of them.
"But we must be not only attend to Rooney but all the big players they have."