Arshavin demanded on Friday that he would want to leave Russia and play abroad.
The 27-year-old was linked with moves to Barcelona, Tottenham and Arsenal in the summer.
“As a coach, I suppose that we should give Andrei a chance to try himself in the other team,” Advocaat told Sport Express.
“It will be better both for our club and for the player.
“We had good time together and it’s time to part with him.”