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.