The centre-back is wanted by Italian Serie A giants Napoli and Sokratis is keen to make the move to southern Italy.
He wants Arsenal to terminate his contract and let him move for free, but so far the Greek defender has been unable to convince the Gunners.
Sokratis has not given up though and, according to Italian daily Corriere dello Sport, is still pushing Arsenal to rip up his contract.
The centre-back made 19 appearances in the Premier League for Arsenal last season, picking up six yellow cards in the process.
He was not involved in Arsenal’s Premier League opener at Fulham on Saturday, which the Gunners won 3-0 thanks to goals from Alexandre Lacazette, Gabriel and Pierre-Emerick Aubameyang.
Sokratis only has a year left on his contract at Arsenal, but the Gunners at present want to earn a fee if he leaves.
The 32-year-old made the move to Arsenal in the summer of 2018.