There are growing claims that the Russian outfit are very keen on making Mancini their next coach if things go wrong for him in Manchester and club officials look for a replacement at the end of the season.
The reports will boost Mancini's standing as he prepares to salvage a season in which City failed to win a game in the Champions League group stage and slipped 12 points behind rivals United in their defence of the Premier League.
Mancini does not want to leave City and believes he can restore the club to glory if the squad is strengthened in key areas this summer, but he will be aware that the rumours linking top names to his job refuse to go away.
Zenit are believed to be on the lookout for a top manager themselves after ex-Roma boss Luciano Spalletti failed to move them forward, despite heavy investment in last summer's transfer market where they signed Hulk and Axel Witsel for a combined £64million.
Zenit lost 1-0 to Rubin Kazan at the weekend and lie in third spot while they must overturn a 2-0 first leg deficit at home to Basel this week if they are to remain in the Europa League.
Mancini was strongly linked to the Russian national team job just before he signed his new City contract last summer and is known to have good contacts in eastern Europe.