"The St. Petersburg forward called the trainer and said that he would not go to the first pre-season camp in the UAE if he was not sold to a foreign club," the paper said.
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, reportedly in excess of $30 million, for the player as "too low."
The club is however believed to have since lowered its minimum price for the player to 18 million euros ($23.8 million).
Zenit recently turned down a $15 million bid, plus a possible $5 million at a later date, for Arshavin from English side Arsenal. The British Sunday Mirror paper also reported at the weekend that Manchester City had agreed a deal to sign the forward. There has been no further news on this possible development, however.
Arshavin has made no secret of his desire to quit his hometown club, and announced last year that if he was not allowed to leave in the winter transfer window then he would remain a Zenit player "on paper only." There are less than three weeks left until the end of the transfer window.
The forward came was named 11th best player in the world by FIFA in its World Player of the Year awards on Monday in Zurich. The title went to Manchester United's Cristiano Ronaldo.