The 31-year-old has fallen down the pecking order at the Gunners this season and is expected to move in the winter transfer window.
Meanwhile, the Royals have made a poor start to the Premier League season and are still awaiting their first victory of the new campaign.
"Arshavin is interesting for Reading. But he is one of 10 players that we are interested in," Zingarevich told Spb.jp.ru.
Arshavin has 75 Russian caps to his name.