Southampton paid a €4m loan fee for Danso but their option to buy him for €8m has now expired.
According to Sky Sport, his disappointing Premier League loan spell has not deterred German clubs.
After making Felix Uduokhai’s loan move from Wolfsburg permanent, Augsburg appear to have no plans for Danso.
Sky reports that Werder Bremen, FC Cologne, Hamburg and VfB Stuttgart are keen on signing Danso.
Werder and Cologne play in the Bundesliga, while Hamburg and Stuttgart are chasing promotion back to the top flight.
RB Leipzig had an interest in Austria under-21 defender Danso in the winter, but have moved on.
Danso is under contract at Augsburg until 2024 and Transfermarkt values him at €6.3m.