The 22-year-old struggled to break into the first team last season under former boss Roberto Mancini, who signed the midfielder from Everton last summer.
"It's a little bit like starting again when a new manager arrives and you have to win him over," Sky Sports News quotes Rodwell as saying. "But that's the same for everyone.
"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."
City are currently third in the Premier League table after two victories and one defeat.