The 30-year-old has struggled for form in north London, and may be tempted by a return to his homeland.
Gunners boss Arsene Wenger has repeatedly claimed that Arshavin is happy at the Emirates Stadium, and remains part of Arsenal's first-team plans.
But with just one goal in 13 Barclays Premier League appearances this term, the Russian captain has failed to make an impression and it is unclear how long Wenger will put up with his under par performances.
And with Zenit prepared to pay Arsenal the full €16.5million they originally paid for Arshavin back in 2009, it could prove to be too good an offer to turn down.
"We are always interested in Arshavin," Zenit director Igor Korneyev told Sovietsky Sport. "But I can neither confirm nor deny whether we have made an offer."
The Russian publication claims that all transfer decisions at Zenit are made by the club's sponsor Gazprom, who are keen to re-sign one of Russia's national heroes.
"The player's return is possible if he decides on it," Gazprom boss Alexei Miller was quoted as saying earlier this month. "We all have to return to our homelands sooner or later."