The 22-year-old midfielder joined Saints on loan for the campaign on August 6, with a view to signing permanently from Inter Milan.
The deal for Taider saw club-record signing Dani Osvaldo go the other way, although his spell at St Mary's has been even more farcical than the Italy international's.
Having been an unused substitute in all three of Saints' matches, it is understood the midfielder is to head back to Italy having failed to settle in England.
Taider did not fit into the group of players or manager Ronald Koeman's worth ethic, meaning he is packing his bags after just three weeks.
The Algeria international is reportedly set to complete a move to Sassuolo, although his departure does not affect Osvaldo's loan deal at Inter.
- Sports & Recreation
- Dani Osvaldo