The South Korea international was signed by Steve Bruce at the Stadium of Light in the summer of 2011 but he has seemingly not impressed successor Martin O'Neill.
Ji has not played this season and is unlikely to feature on Tuesday night against Queens Park Rangers as goal-shy Sunderland have preferred the combination of Stephane Sessegnon and £12million August signing Steven Fletcher.
Augsburg have already sounded out the 21-year-old about a January loan as the Bundesliga's bottom club looks for goals to save them from relegation.
Augsburg general manager Jurgen Rollmann told Augsburger Allgemeine Zeitung newspaper: "This (Ji) is an interesting player for us. We have also been in touch with him.
"But we haven't yet put up an offer for him."