According to Bild, the Gunners are ahead of the likes of Manchester United and Juventus because Arsenal's head of recruitment, Sven Mislintat, is in "close contact" with the centre-back's agent, Konstantinos Farras (h/t Football.London's Charles Watts).
The 29-year-old, who has one year remaining on his contract, is expected to cost around €20 million (£17.5 million). It's said to be "probable" that he arrives at the Emirates Stadium this summer.
Mislintat's primary focus for the upcoming window is to secure a centre-back, a goalkeeper and a central midfielder in order to strengthen the Gunners' spine.
Arsenal's defensive frailty has repeatedly let them down this season. The north London outfit has shipped 46 goals in the Premier League—14 more than seventh-place Burnley—and on Thursday, they allowed themselves to be sucker-punched by Atletico Madrid despite dominating the 10-man side for the majority of their UEFA Europa League semi-final first leg.
As sports journalist Mootaz Chehade noted, Nacho Monreal, Laurent Koscielny and Shkodran Mustafi were all at fault:
Mustafi has been a liability since he arrived from Valencia in 2016, while Koscielny's time at the top level appears to be over, particularly as he will turn 33 in September.
According to Squawka, Sokratis has won 43 tackles, 70 headed duels, made 35 interceptions and 98 clearances in 27 Bundesliga appearances this season. He has also maintained a passing accuracy of 87 per cent, created five chances and scored twice.
Goal's Ronan Murphy and football writer Lars Pollmann have their doubts about the Greece international, however:
With manager Arsene Wenger departing this summer, the Gunners' goal will be to reverse the decline the Frenchman has overseen in recent years. Strengthening their spine—particularly their defence—could help them achieve that.
That process will not occur overnight, but it's vital they get their recruitment decisions correct in order to expedite it. Sokratis has mostly impressed with BVB, but his signing could be a risk Arsenal can ill afford to take.