The Zenit St Petersburg star, 27, wants to quit his homeland for a crack at a bigger league after lifting the UEFA Cup last season.
The Gunners are claimed to have lodged an offer of around £10m but with mega-rich City able to blow them out of the water, any transfer will come down to the player's ambition, or desire to seek massive wages.
Zenit spokesman Alexei Petrov told the Mail on Sunday: "I can confirm that Zenit did get an official offer from Arsenal about Andrei Arshavin. It was rejected as insufficient."
He added: "They offered about £10m. No new offers have arrived from them since. At the moment, Arsenal are the only club to have approached us about the player."