The Blues see Sosa as a replacement for wantaway fullbacks Cesar Azpilicueta and Marcos Alonso.
Heidenheimer Zeitung says Stuttgart have "assured" Sosa that he will be allowed to leave this summer.
And the Bundesliga outfit are willing to accept a bid of £21m.
No concrete bid has yet been submitted by Thomas Tuchel's side, although they are thought to be open to spending up to £24m for the Stuttgart man.
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