First-choice candidates Di Matteo and Poyet are said to be lukewarm about taking the job.
Both the current favourites for the vacant managerial post at the Stadium of Light are understood to be reluctant to take over from the recently sacked Paolo Di Canio as the next Sunderland boss, according to reports in the Guardian.
Former West Bromwich Albion and Chelsea manager Roberto Di Matteo and ex-Brighton and Hove Albion head coach Gus Poyet have emerged as the two favourites to replace the Italian in the north east after Di Canio was given the boot by Black Cats owner Ellis Short on Sunday.
Di Canio left his position at the Stadium of Light with Sunderland propping up the Premier League table having collected just the one point so far from their opening five games of the top-flight season, with the final straw coming at the Hawthorns on Saturday afternoon when Sunderland surrendered meekly to the Baggies in a dispiriting 3-0 reverse.
As a result, an emergency board meeting was called for Monday by Short, where a list of possible candidates to succeed the fiery Italian were discussed, with Sunderland director of football Roberto De Fanti understood to favour a manager with experience of the Premier League, but crucially also one that is currently out of work to ease the process.
However, the Italian may be scuppered in his efforts to appoint either Di Matteo or Poyet after it emerged that both men had serious reservations about taking on such a high-risk role, which may now open the door for former England coach Steve McClaren to make a return to football.