Despite winning the league and League Cup last season, Pellegrini has failed to improve the squad's fortunes this campaign.
They are on the verge of exiting the Champions League and need to overhaul a 3-1 first-leg defeat to Barcelona on Wednesday, are out of the FA Cup and failed to win the League Cup.
Meanwhile, defeat at Burnley yesterday saw them slip further behind Chelsea, who Benitez took to Europa League glory in 2013.
Benitez is expected to leave Napoli this season and although there are reports in Italy claiming he could take over from Filippo Inzaghi at Milan, City appear the most likely destination.
Pellegrini: Man City lacked creativity [AMBIENT]
The 54-year-old won the Champions League and FA Cup while boss of Liverpool before being sacked in 2010 and last season he won the Coopa Italia with Napoli.
Earlier this week Benitez himself discussed his future, stating: “Today I’m in Naples and I’m concentrated on Napoli.
“But in the future I can’t predict what will happen. In the past I’ve coached in Spain, England and Italy.
"I think Ligue 1 is full of good players, who are very fast and well coached in a technical sense.
"However, the mastery of tactics is less developed than in Serie A, and the tempo is slower than the Premier League.
“I’d have no problem embracing a new adventure in a new league. There’d have to be the right offer, at the right time, with the right team.”
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