The underachieving Bundesliga outfit are planning to strengthen their defence with the Greek defender, however they also face competition from former club Genoa
Sporting director Klaus Allofs sees the Greek international as the ideal candidate to strengthen their traditionally weak defence.
With Per Mertesacker out until July, Naldo a long-term casualty with a serious knee injury and the departure of Finnish international Petri Pasanen, Werder are in need of defensive reinforcements as they look to improve on this season's 13th place finish.
"There are still a number of things to clear up. However, I would think that we will know more in the coming week," Allofs told Bild about the club's interest in the player.
One potential problem for Thomas Schaaf's men is the interest from Sokratis' former club Genoa, who, according to the player's agent Nikos Klitsidis, are looking at bringing him back to the club.
"We are aware of the interest from Werder Bremen but in the next few days certain things must be clarified first with Genoa," Klitsidis commented.
The 22-year-old stopper has made 20 appearances for Greece, but made just five outings during Milan's title-winning Serie A campaign and the Grifone regained 50 per cent of the player's rights as part of Kevin Prince Boateng's full transfer to the Rossoneri this summer.