Skrtel joined Liverpool from the Russian side in 2008.
The Daily Mirror reports that Zenit have set aside around £16million to land Skrtel in the January transfer window.
Skrtel has forced his way back into the first-team plans at Anfield after having been dropped during the second half of last season by manager Brendan Rodgers.
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Chelsea have struggled to build momentum in the opening stages of the campaign and are currently looking over their shoulders at the relegation zone.
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