The Serbia international joined on a two-year deal in August 2016 and played 21 games for the Championship side.
But the 34-year-old's last appearance for Forest came in February and he has not featured since Mark Warburton took over as manager in March.
Jordan Smith has started the season as Forest's number one keeper with Dimitar Evtimov on the bench.
Stephen Henderson is still recovering from an Achilles injury.
Stojkovic's last two competitive appearances came in World Cup qualifiers, against Georgia in March and Wales in June.
Goalkeeper Vladimir Stojkovic has left Nottingham Forest after his contract was cancelled by mutual consent.