Jordaan is president of the association and led the country's World Cup bid committee which secured the rights to host one of the biggest sporting events in South Africa in 2010.
His arrest follows a raid by the country's Special Investigating Unit at the offices of SAFA in March "where an assortment of electronic gadgets and files were seized for further investigation, thus leading to the arrest,” police spokesperson Katlego Mogale said.
According to the police, Jordaan was arrested with one other official and a businessman. They are expected to appear in the Palm Ridge Magistrates Court on Wednesday.
SAFA did not immediately respond to requests for comment.
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