The 22-year-old was bought Everton at the beginning of last season by then-manager Roberto Mancini, but only managed to make 11 league appearances.
Rodwell's poor record was partly responsible to a number of injuries, including a recurring hamstring problem.
But after fighting back to fitness once again, he is prepared to make his mark on Pellegrini and keep himself in the mind of England manager Roy Hodgson.
"It’s a little bit like starting again when a new manager arrives and you have to win him over," he told the Daily Star.
"But that’s the same for everyone. The previous manager Roberto Mancini brought me here, and obviously I was a little bit sad to see him go.
"But that’s football. Obviously Manuel Pellegrini is a great manager and I’m happy to see him come in as well so 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."
Rodwell, who missed out on a place in the England squad for their upcoming FIFA World Cup qualifiers against Moldova and Ukraine, is yet to feature for Pellegrini in the new season but will hope for his chance when the club play Stoke City after the international break.
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