The Budesliga outfit are keen admirers of Papastathopoulos and hope to sort out a deal for the defender in the near future despite complications over the player's rights. Milan and Genoa co-own the Greece international.
"We are trying to find a solution," Bremen's director of football Klaus Allofs told Kreiszeitung.
"Italy is special because clubs often share the rights to a player, just as is the case with Sokratis being owned by AC Milan and Genoa.
"The player lies in the middle and he has a veto. We would not be pushing so hard to sign him if we did not have a clear signal from him that he wants to join us."
Papastathopoulos joined the Rossoneri last season but has only made five league appearances for them so far. However, he did make over 50 appearance for Genoa following his move from AEK Athens in August 2008.