The 32-year-old joined the Gunners from the Russian outfit for €16.5 million in 2009 but, after a bright start, has since lost his place in Arsene Wenger's first-team squad and has become a peripheral figure this term.
And following confirmation that Arshavin would not be offered a new deal at the Emirates Stadium, Spalletti would welcome the 32-year-old back to Russia amid reported interest from clubs in Turkey, United States and the Middle East.
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"I believe there is a commitment within the club as a priority for a possible return to Russia, but I can't say whether there have been any negotiations."
Arshavin had a loan spell back at the Petrovksy Stadium in 2012 and could be part of a large scale clear-out by the Gunners in order to reduce their sizeable wage bill.
The former Russia international has 11 appearances for the Gunners this season, scoring once in the Capital One Cup.