The Russian giants have been keeping close tabs on the 22-year-old footballer for quite a while and they recently decided to make their interest concrete.
According to Izvestia, Zenit were prepared to offer around €20 million for Firmino last summer, but Hoffenheim refused to sell their star player at the start of the season.
Nevertheless, it appears that the Sky Blues are ready to return for the highly rated attacker, although it looks they will not have enough time to complete the deal before the winter transfer window closes.
Roberto Firmino, who has bagged 11 goals in 21 league matches this season, has a contract until June 2015, meaning he is likely to be available for sale next summer.
Zenit are currently tied on points with Lokomotiv Moscow at the Russian Premier League summit and they are the number one favourites for the league trophy.