Sokratis appears to be nearing the end of his Arsenal career as the defender leans towards a potential move to Genoa.
The 32-year-old's contract at the Emirates Stadium expires in the summer and he emerged as a target for the Italian side at the start of the transfer window.
Fenerbahce have also been linked with Sokratis but according to Sky Sport Italia the defender would be keener on a move to Genoa should the clubs' financial terms offered to the player be similar.
Should the Greece international move to Genoa, it would be his second spell at the club having previously played there between 2008 and 2010.
They are on the lookout for a centre-back after a move for Lazio's Denis Vavro fell through to due to concerns over his fitness following a medical.
Sokratis has been frozen out of the first-team at the Emirates Stadium this season with manager Mikel Arteta opting not to select him in either his Premier League or Europa League squads.
He joined the Gunners from Borussia Dortmund for £17million in 2018, making 69 appearances in total.
However he quickly fell out of favour under Arteta following his appointment just over a year ago.
Since March prior to the first lockdown, he has played just three minutes - all coming as late substitutes including in the FA Cup final against Chelsea back in August.
Arsenal have already turned to the future with their centre-backs, having confirmed their first signing of the window in the shape of Omar Rekik from Hertha Berlin.
Following his £540,000 move the 19-year-old will move straight into the Under 23s squad to aid his development.