The report claims that the outgoing City boss is looking for a new experience and has attracted strong interest from Russia, with Zenit set to make a concrete offer for the Chilean in the summer.
Pellegrini joined the Citizens in 2013 having had previous success in Spain with the likes of Villarreal, Real Madrid and later Malaga who he led to an impressive Champions League quarter-final spot.
In his three seasons at the Etihad Stadium, he has won the Premier League title once and experienced two League Cup successes with the latter come via a penalty shoot-out win over Liverpool.
But despite his popularity, Pellegrini is to be replaced by Pep Guardiola this summer with the decision being made official in January, leaving the Chilean in a tough situation as he looks to end the season with dignity.
Zenit, currently under the guidance of Andre Villas-Boas, won the Russian championship last term and reached the knock-out stages of the Champions League this year.
However, the Portuguese boss is to step down this summer after three years in charge, leaving the club looking for a new boss and eyeing Pellegrini as a potential replacement.
The 62-year-old could probably find a top job in one of Europe’s five major leagues, yet the financial gains in Russia and the less-taxing league campaign may be too tempting to pass up.