"The association welcomes the investigation and is working very closely with Fifa to ensure that the scourge of corruption is uprooted from the game," Safa said in a statement on Monday.
"Fifa also briefed the association about the various risk factors that all associations need to be on the lookout for and to mitigate," Safa said.
"These include, but are not limited to, illegal online betting, match fixing, irregular player registrations and age cheating."
Safa added that Fifa was "pleased" it had discontinued the practice of engaging agents to source referees for matches played by SA national teams.
"The Association took a decision to revert to appointing referees itself through Caf [Confederation of African Football], or in the case of friendly matches, through our sister football associations, as this will ensure full control and integrity of outcomes of all matches."
Fifa confirmed, according to Safa, that it was not investigating the association or any of its members but was interested in getting information about the referees linked to the investigation.