The 34-year-old is currently training with the Premier League side.
David Moyes has told the Shields Gazette that he has been impressed with Steven Pienaar since the midfielder came to Sunderland on trial, but admitted that he needs another week to make his mind up about whether to offer him a deal at the Stadium of Light.
The 34-year-old is a free agent after leaving Everton at the end of last season. And with the Shields Gazette reporting that the Black Cats are in need of adding depth in the middle of the park - Seb Larsson is out for around six months while Jan Kirchhoff and Lee Cattermole are also struggling with injury - it seems like it could be a good bit of business for Moyes to sign the South African on a short-term deal.
Sunderland manager David Moyes
But while he confirmed that he was pleased with what he had seen from Pienaar, he insisted that he needed more time to make a decision about whether to sign him or not.
"Steven is still here – he has done very well," he told the Shields Gazette.
"We thought about maybe including him in the Under-23 game on Sunday, but we will probably train him more and get him ready.
"He is very good on the ball, doesn't give possession away too often.
"He is a tidy player but we would probably rather wait another week or so to see where he is at.
Though the former Tottenham man struggled to make any impact during his final year at Goodison Park, he could perhaps be a good option to have amongst the squad.
Having arrived at Sunderland quite late in pre-season, Moyes has perhaps not had as much time as he would like to work on finding targets before the new campaign begins.
Therefore, he may have been tempted to turn to players he already knew well in the hope that they can keep the club afloat until next summer when he will be looking to really make his mark on the squad.
Pienaar surely enjoyed the best football of his Premier League career when he was playing under Moyes during his first spell with the Toffees, and Moyes may be hoping to see glimpses of that player during the coming week as he will then know that he still has plenty to offer his side.