Anzhi officials were in Milan on the weekend, but Zenit coach Luciano Spalletti has now declared their interest in the Dutchman.
"Who wouldn't want him? But he'll be hard to tear away from Inter," said Spalletti.
Zenit are willing to match Anzhi's €8 million-a-year net offer to Sneijder. But Mediaset says the midfielder still has hopes of joining Manchester United at the end of this season.
The Russian transfer market doesn't close until February 24.