The England international midfielder, who is in the last year of his current deal, fears a new contract is not forthcoming at the Etihad Stadium.
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"It depends on what he wants ... we have also Rodwell, Garcia, Fernandinho and they are here today," Pellegrini told reporters.
"But I spoke with Gareth, he wants to stay here. He doesn't have any problems to stay here. He will fight for his position as [with] any other player in the squad.
"If he wants to go because he has better options it depends on what he wants to do."
Barry has made 132 appearances for Manchester City since joining in 2009, scoring six goals.