Arshavin joined Zenit on loan in February after finding himself down the pecking order at the Emirates Stadium.
The 31-year-old, who has scored three goals in nine starts for Zenit, is set to discuss his future at Arsenal at the end of Euro 2012.
Zenit are ready to discuss a permanent deal with the Russia captain, but they insist any move depends on Arshavin.
"Everything depends on Arshavin. If Andrey is ready to stay in the team and go on the field as a player, we are ready to discuss it," said Zenit chief executive Maxim Mitrofanov.
"Arshavin is part of our club but, with all due respect to him, he will only stay in the event that he proves himself useful as an active player. Not as a man making up the numbers."
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