The centre-half is wanted by Italian Serie A heavyweights Napoli and Sokratis is keen to seal the move to southern Italy.
He wants the board to terminate his contract and let him move for nothing, but so far the Greek star has been unable to convince the Gunners.
Sokratis hasn’t given up though and, according to an Italian daily Corriere dello Sport, is still pushing the Gunners to rip up his contract.
The centre-back made 19 appearances in the English top-flight for Arsenal last season, picking up six yellow cards in the process.
He wasn’t involved in Arsenal’s Premier League opener at Fulham last week, which the Gunners won 3-0 thanks to goals from Pierre-Emerick Aubameyang, Gabriel and Alexandre Lacazette.
Sokratis only has a year left on his current deal at Arsenal, but the Gunners at present want to earn a sum if he leaves. He made the move to Arsenal in the summer transfer window of 2018.
Elsewhere, Arsenal are reportedly ready to allow Lucas Torreira to leave the club, with Torino and Fiorentina both looking to strike a loan deal for the star.
Torreira struggled to impress at the Emirates last campaign, with the midfield pairing of Dani Ceballos and Granit Xhaka being preferred by Arsenal manager Mikel Arteta.
Furthermore, the club have also welcomed Mohamed Elneny back into the fold, while highly-regarded duo Thomas Partey and Houssem Aouar are both being mentioned with moves to the Emirates Stadium.
As a result, The Guardian states that Torino and Fiorentina are set to battle it out for Lucas’ signature, and the Gunners are open to a loan or permanent departure for the 24-year-old.