Kevin Ball has been in interim charge for more than a fortnight since the dismissal of Paolo Di Canio and he has overseen a League Cup win over Peterborough and Premier League defeats by Liverpool and Manchester United.
Poyet, who lost his job at Brighton at the end of last season, has been the firm favourite for the permanent post for more than a week with the bookmakers.
Owner Ellis Short had promised to take his time over the appointment as he looks to bring some managerial stability to the club. Roberto Di Matteo, Tony Pulis and Gianfranco Zola are others to have been linked with the job.
Sunderland are bottom of the standings, having collected just one point - from a 1-1 draw at Southampton - in their opening seven games.
Poyet won 86 of his 194 games as Brighton manager, leading them from League One to the Championship play-offs last season, where they lost out to Crystal Palace.
Sunderland owner Short insisted at the weekend that staying in the Premier League was vital and great care would be taken to ensure the right man was brought in.
"Here at the club, like every supporter, we would like to see long-term success on the pitch and stability at the club," Short said in his matchday programme notes ahead of the clash with Manchester United.
"Unfortunately sometimes the quest for stability can be interrupted by the absolute necessity of staying in the league.
"This is because the long-term aim becomes irrelevant if we aren't at the top level.
"We now have a very important decision to make. Our only consideration in making that decision is what is best for the club. In doing so, we feel the weight of the entire city and beyond, along with the history of this massive football club.
"The appointment of a replacement head coach is our priority and I urge you to ignore the speculation in the media about the selection process, because most of it is completely wrong."
Ball admitted after the loss to United that he had 'no idea' when an appointment would be made, but did say that he felt the team had made progress since he took charge.
He said: "There are standards I have spoken to them about in training. They have worked hard, but there are still a lot of areas to improve on."