Reports claim the Russian side are ready to make a bid for the winger in the January transfer window.
Walcott’s current contract with the Gunners is set to expire at the end of the season and the winger has so far refused to extend his deal.
The winger has previously been strongly linked with a number of Premier League and Serie A clubs.
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Since Guus Hiddink arrived at the helm, Chelsea have improved considerably after a tricky start to the campaign.
Newcastle United are staring down the barrel of relegation to the Championship for the second time in the past eight years.