Zenit boss Luciano Spalletti is desperate to sign a new central defender before the close of the transfer window, and has identified Astori as his number one target.
The 27-year-old has been heavily linked with a move to Manchester United, after David Moyes personally flew out to watch him in action against Juventus earlier in the month.
Moyes is in the market for a new centre back, with both Rio Ferdinand and Nemanja Vidic out of contract at the end of the season, and both expected to leave Old Trafford.
Southampton have also held a long standing interest in the Italian international, with boss Mauricio Pochettino thought to be lining up a last-minute January bid.
The Saints have been rocked by the news that Dejan Lovren is facing a lengthy spell on the sidelines with an ankle injury, which may well force Pochettino into the transfer market before Friday’s deadline.
But the two Premier League clubs will now have to battle wealthy Zenit, who are preparing a bid of their own, according to reports in Russia.