Chelsea owner Roman Abramovich was in the stands during Euro 2008 as Arshavin inspired Russia’s progress to the semi-final stage.
And reports claimed Abramovich was keen on bringing the Zenit St Petersburg star to Stamford Bridge this summer.
However, after new manager Luiz Felipe Scolari made Portugal playmaker Deco one of his first signings at Chelsea, the club’s interest in Arshavin has cooled.
"I do not believe that after this acquisition of Deco the club have retained their interest in Arshavin," said Dennis Lachter, Arshavin's agent.
Lachter added: "Zenit want to get at least €30 million (£23.8 million), and foreign clubs offer no more than €20 million (£15.8 million).
"The situation is not at an impasse though. The transfer period only ends on August 31 and clubs are only just beginning to be proactive in the transfer market."
During Euro 2008, Arshavin expressed his desire to join Barcelona, though transfer activity at the Nou Camp is currently being disrupted by the club's presidential elections.
Chelsea meanwhile, could be set to sell defender Branislav Ivanovic to Juventus.
The 24-year-old Serbia international signed for Chelsea from Lokomotiv Moscow in January but has failed to break into the first team.
And Juventus manager Claudio Ranieri is reportedly ready to spend £12million on taking the defender to Turin.
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