Arshavin, 27, was linked with a number of clubs, including Barcelona and Tottenham, in the summer after leading Russia to the semifinals of Euro 2008. However, Gazprom-controlled Zenit subsequently turned down a number of offers for the player as "too low."
Arshavin has made no secret of his desire to quit the club, and recently announced that if he was not allowed to leave in the winter transfer window then he would remain a Zenit player "on paper only."
"The club has give Arshavin permission to hold talks with other clubs," Zenit's general director Maxim Mitrofanov told the paper, noting that, as a rule, players under contract, "have no right to do this."
"We will consider any forthcoming offers," he said.
The transfer window opens on January 1. Although no new bids have been made for Arshavin, who recently came sixth in a poll to find the European Footballer of the Year, media reports have said that a number of clubs, including AC Milan, are preparing to make offers for the Russian international.
