The Chilean has already revealed that he will leave current club Malaga at the end of the season and has now spoken of his potential move to England for the first time
The 59-year-old is City's first-choice candidate to replace Roberto Mancini, who was sacked with two Premier League games remaining earlier in May.
Pellegrini has already revealed he will leave Malaga this summer for "sporting reasons" but has, until now, remained coy over his next destination.
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The 59-year-old quickly emerged as the favourite to take over at the Etihad Stadium for the start of the new season even before Mancini was relieved of his duties, with details emerging of meetings between City and Pellegrini's agent on the morning of the FA Cup final.
However, City's demoralising defeat to Wigan Athletic at Wembley capped off a disappointing final season under Mancini, in which the club easily conceded their Premier League title to city rivals Manchester United and failed to progress from their Champions League group.
Those failures, coupled with reports of Mancini's man-management skills beginning to fail with his players, eventually sealed the Italian's fate.
Should Pellegrini arrive at City, there have also been reports that he will bring star Malaga midfielder Isco with him to the Etihad.