Sunderland gave Pienaar a one-season contract at the start of the 2016/17 campaign, but the Black Cats have had a dreadful season and their relegation was confirmed after defeat at home to Bournemouth this weekend.
Pienaar was courted by Orlando Pirates, among others, when his contract at Everton ran out at the end of last season, and may now decide it is time to return home for a career swansong.
Chiefs were also said to be interested in signing the 35-year-old midfielder, but the club’s football manager Bobby Motaung dismissed those reports.
Sundowns are believed to be keen on signing Pienaar.
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