The 22-year-old has struggled to make an impact for City after being signed in a £12million deal from Everton by former manager Roberto Mancini last summer.
Frustrating injury problems contributed to Rodwell making just 11 Premier League appearances last term and he is yet to feature in the current campaign.
With Pellegrini having invested heavily in the summer transfer window to add even more talent to City's star-studded squad, the England hopeful knows he faces a battle to secure a spot.
"It's a little bit like starting again when a new manager arrives and you have to win him over," Rodwell told reporters. "But that's the same for everyone.
"The previous manager brought me here and obviously I was a little bit sad to see him go. But that's football.
"Manuel Pellegrini is a great manager and I'm happy to see him come in. Everyone is in that position where they want to win him over and I'm no different.
"I think everyone feels it's a fresh challenge more than anything. Everyone has come in and is trying to win the manager over, which has brought a new lease of life.
"It's a 25-man squad, where every player could pretty much walk into any other Premier League team. That gives you an indication of the strength of it. But I'll be fighting for my place.
"Playing for England is something I dreamed about and going to a World Cup finals would be fantastic."