The 24-year-old is free to leave the John Smith’s Stadium, but striker Ishmael Miller is among eight other players who have accepted extended deals.
Gobern made a total of 79 appearances for Huddersfield, scoring three goals, after joining on a free transfer from Southampton in June 2011. He has had loans spells with MK Dons and Chesterfield.
Miller, 28, joined Huddersfield on a short-term deal from Blackpool in February and scored three goals in 16 appearances.
Midfielders Duane Holmes, Joe Wilkinson and Ben Holmes, striker Flo Bojaj, defenders William Boyle and Joe Wright, plus goalkeeper Sam Guthrie have all had their contracts extended.
Goalkeeper Ed Wilczynski has been offered a new deal and first professional contracts have also been offered to academy scholars Tadhg Ryan, Fraser Horsfall and Jack Senior.