The Premier League side were linked with the Swedish international over the summer, with Brendan Rodgers rumoured to be keen on strengthening his defensive options.
However, reports have emerged that the big spending Russians are now keen on the centre-back and could make a swoop during the January transfer window.
The Italians are believed to value their man at around £6.5m, which would be small change for Zenit who splashed a combined £70m to bring former Chelsea target Hulk and Belgian midfielder Axel Witsel to the club earlier this year.
The 27-year-old is rumoured to be keen on a switch to Anfield, but the Saint Petersburg-based outfit are likely to offer him a very lucrative deal to swap Serie A life for the Russian Premier League.
Granqvist spent the 2008/09 season with Wigan, moving to the DW Stadium from Helsingborgs in his homeland.
He failed to hold down a starting berth with the Latics, making just over ten appearances before moving to Eredivisie outfit Groningen.
Since his forgettable spell in the Premier League the Swede has forged a reputation as tough-tackling, reliable defender and made almost 30 appearances for his national team.