The 24-year-old is a free agent after leaving Hamburg SV after seven years at the club.
Greuther Fürth are interested in bringing the German-born Ghanaian defensive midfielder to the Trolli-Arena.
The Bundesliga II side are looking for reinforcements following the departure of Paul Jaeckel to Union Berlin and Mergim Mavraj whose contracted was not extended.
The enterprising defender had a torrid 2020/21 season in the Bundesliga due to injuries featuring 19 times in all competition for the side.
Jung was tipped to reach the top after bursting onto the scene in the 2015/16 season in Bundesliga, however, he is struggling to get there due to persistent injuries.
In 2017, Jung celebrated the European Championship title with the German under-21 team. But he is still eligible to play for Ghana.