Svanberg's current deal runs out in 2027, but with VfL Wolfsburg relegated last season he faces the prospect of playing his football in 2. Bundesliga unless a move materialises before the transfer window closes.
According to Wolfsburger Allgemeine Zeitung, Werder Bremen are keen to sign the 27-year-old this summer, though the German outlet DeichStube reports that Bremen's interest is conditional on Jens Stage first leaving the club, with the Danish midfielder currently being pursued by TSG Hoffenheim.
Bremen finished one place above Wolfsburg last season and avoided the relegation play-off as a result, a fine margin that now leaves them in a position to potentially benefit directly from Wolfsburg's drop down a division.
Bild is reporting that Wolfsburg have set a price tag of €4m for Svanberg, though it remains unclear whether any concrete bid is currently on the table.
It is equally unclear how Svanberg himself views a possible move. The Swede was unable to reach agreement over personal terms with Galatasaray when a switch to Turkey was on the cards last winter, with reports at the time suggesting the Turkish club's own supporters pushed back against the deal in hope of a more high-profile alternative arriving instead.
Svanberg has made just over 100 Bundesliga appearances for Wolfsburg since joining from Bologna in 2022, scoring 11 goals and providing 12 assists during his time at the club.
Wolfsburg's relegation marked the first time in the club's history that they have dropped out of the Bundesliga, and with Svanberg's contract entering its final year, this summer represents likely the last realistic opportunity for the club to recoup a meaningful transfer fee for the midfielder rather than risk losing him for nothing next year.
Werder Bremen, for their part, are understood to be weighing up several midfield options as they prepare to potentially lose Stage, with Svanberg regarded as a relatively low-cost, experienced alternative given his familiarity with German football.