Manchester City would be interested in signing Raheem Sterling if he were to become available, according to Sky sources.
Tottenham have completed a deal for Cologne defender Kevin Wimmer and he will join them in June, Sky sources understand.
Hackett, 29, made 145 appearances for the Lions, scoring five goals, since joining from Hearts in 2006.
However, he slipped out of the first-team picture this season and ended the campaign on loan at Wycombe.
Former Leicester and Watford full-back Stewart, 30, endured an injury-hit season since he signed last summer and managed just seven appearances.
Youngsters Jake Gallagher and Conor McLaren have also been released.