Pellegrini is due to be replaced by Pep Guardiola at the end of the season and following the confirmation has been linked with a host of clubs across Europe.
Zenit are reportedly ready to offer the Chilean a two-year deal worth €4million-per-season (£3.09million) after speaking to his agent about a potential move.
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However, the 62-year-old is keen to stay in the Premier League after settling in England and would consider taking a job outside of the Champions League.
Pellegrini was also once linked with the vacant Chelsea job, but the club's interest in appointing Antonio Conte appears to have ruled out such a move.
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And in somewhat surprising circumstances, this could lead him to Newcastle United, who are believed to be tickling the City manager's fancy. The Magpies are battling against relegation and could sack Steve McClaren should results not improve.
La Liga side Valencia are also reportedly interested in bringing Pellegrini back to Spain, where he has previously managed Villarreal, Real Madrid and Malaga.
Since joining City in 2013, Pellegrini has won two Capital One Cup's and the Premier League once, during his debut season in charge.
Fans regard reclaiming the English crown this campaign as the perfect send-off for the Chilean, but following defeat to Liverpool on Wednesday, which left the Citizens ten points behind league-leaders Leicester City, this appears unlikely.