BBC journalist David Ornstein has revealed that the Gunners already have one expected defensive deal wrapped up while another signing is being worked on.
The Gunners have been eager to get much of their summer transfer deals done before the World Cup begins since the prices of players could potentially change dramatically after the tournament in Russia.
New Arsenal manager Unai Emery has been tipped to be busy ahead of next season as he prepares his side for another campaign which will see them compete in the Europa League instead of the Champions League after their failure to finish in the top four of the Premier League last term.
Following the arrival of Stephan Lichtsteiner last week, there have been rumours claiming that Sokratis is on his way to the Emirates stadium as well.
According to David Ornstein, the 29-year-old, who has been pocketing £90,000-a-week wages in Germany, has indeed left Dortmund for Arsenal and the deal will be announced next month.
The BBC journalist also added that the Gunners are working on signing Sampdoria midfielder Lucas Torreira as well.