The Russian has found himself playing a bit-part role for most of the season at the Emirates with Arshavin admitting his performances have been 'average'.
Anzhi Makhachkala have been credited with an interest in Arshavin, but the diminutive attacker insists he has had no contact with the wealthy Russian outfit.
"Right now I don't think about changing clubs. If I will be benched for a very long time, then such an issue might be relevant," Arshavin told Sport Express.
"I still want to play for 90 minutes, but now I am glued to the bench. I wouldn't like to play for a Russian club other than Zenit [St Petersburg], and there were no contacts with Anzhi Makhachkala."