The defender is out of contract at the Stadium of Light at the end of this month, but Sunderland are keen to keep him in their ranks.
Sunderland offered Wright a new deal following their promotion back into the Championship but he was yet to give a decision on his future.
The Australia international has attracted interest from two A-League sides and he has been vocal about his desire to someday play in his homeland again.
But Wright is now set to put pen-to-paper on a new deal at Sunderland, which is welcome news for boss Alex Neil.
Danny Batth is the only senior centre-back currently available to Neil but Wright is now set to continue to be an option at the back.
Despite a slow start to his campaign last season, Wright managed to nail down a starting role at Sunderland and played an integral role under Neil in their promotion-winning run.
Sunderland still want more additions at centre-back and have submitted an offer for Arsenal starlet Dan Ballard.
