The former Everton star has been on trial with the Black Cats since early August as manager David Moyes and his technical team run the rule over him.
'Schillo' has been a free agent since being released by Everton at the end of the 2015/16 campaign.
Moyes and Pienaar enjoyed a successful working relationship during their time together at Goodison Park, and it's thought that if the attacking midfielder can prove his fitness, he will more than likely be offered a deal on Wearside.
It was expected that Sunderland would play the former Bafana Bafana captain in a pre-season friendly against Borussia Dortmund in Austria yesterday, but the club's management opted to leave him behind in England to work on his fitness.
The North East outfit have now confirmed that they will further assess Pienaar on Monday before making a final decision on his future.
The club's assistant manager, Paul Bracewell, told the Sunderland Echo: "Steven came in at the latter end of the week and he stayed behind to work with the fitness coaches, so we need to catch up with the rest of the staff on Monday to see how he is."
Positive news for the South African is that Sunderland have confirmed experienced French left-winger, Charles N'Zogbia, will not be offered a deal after an extended trial. This potentially means less competition in his playing position at the English Premier League team.