Wolves' Bakary Sako has revealed he is mulling over offers from the Premier League but is yet to decide on his future.
Rotherham boss Steve Evans will decide the fate of his out-of-contract players in a meeting on Monday.
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.