Arshavin has fallen out of favour in North London, failing to make a single Premier League start this season and notching up a total of just 11 appearances.
Reports in Russia suggest clubs in Azerbaijan and Australia have their eye on the 31-year-old, whose contract with the Gunners is due to expire in the summer.
Yalchin Aliyev, a spokesman of Azerbaijan club Khazar, says his side are among four of the country's Premier League sides who have the funds to try and tempt Arshavin.
Former Wales boss John Toshack recently took over as manager at the club and Aliyev says the manager will consider which areas of his squad need strengthening.
He told izvestia.ru: "At the moment there are only four teams in Azerbaijan who could be ready to pay for such a player as Andrey.
"Apart from Khazar it's Quabala, Neftci and Baki.
"We have a new coach: the popular John Toshack. At the moment he has to check the squad and decide in which positions he should strengthen the team."