The League One outfit ended their one-year association with Phil Parkinson this week, handing first team coach Andrew Taylor the reins temporarily.
Sunderland have begun their hunt for a new boss to take charge of the club and a number of names have been touted as possible options.
Former Black Cats manager Poyet has been named as the favourite to replace Parkinson at the Stadium of Light.
However, contrary to claims he could take over again, the Uruguayan tactician will not be making a return to the Wearside-based club.
Although he is currently without a club, Poyet would prefer not to drop down to League One, something which rules him out of taking the job.
Poyet was at the helm of Sunderland between 2013 and 2015 when they were plying their trade in the Premier League.
It is claimed that he was on the club’s radar, but will not be returning.
Since leaving Sunderland, Poyet has had spells in charge of AEK Athens, Real Betis, Shanghai Shenhua and Bordeaux.