The forward held talks before leaving with Advocaat and Alexander Dyukov, the Zenit president, at which he was told that the club were ready to accept an improved Arsenal offer.
The Arsenal board are believed to have tabled an initial bid of £8 million – despite Zenit's valuation of £20 million. They have since raised their offer to £15 million. Advocaat admitted: "Negotiations with Arsenal continue, and the chances are very high that Arshavin will soon play in the Premier League."
Zenit's change in attitude has been brought about largely by their acquisition of Portugal striker Danny from Dinamo Moscow, for a Russian transfer record of £30 million, which should sharpen their side's attack even in Arshavin's absence.
The transfer represents a substantial coup for Arsenal in light of the interest already expressed in Arshavin by Manchester City and Inter Milan.
Manager Arsene Wenger, who has remained evasive on the subject of Arshavin, has acknowledged progress in Arsenal's search. "I'm very hopeful, in days, yes. We are not close to signing but we know what we want to do."
Wenger has also disputed suggestions that AC Milan would bid for his two top strikers, Emmanuel Adebayor and Robin Van Persie, in the event of selling Kaka to Manchester City. "I'm not worried about that at all," the Frenchman said.