South Korean newspaper Chosun Ilbo reported on Monday that South Korean police could charge Chung with obstruction of business for appointing German Jurgen Klinsmann as national team head coach by himself.
Previously, the Public Welfare Committee filed a complaint against the KFA chairman.
The committee accused Chung of interfering in the work of the association officials, forcing them to approve Klinsmann as the new coach of South Korea.
South Korea's poor, lackluster performance under Klinsmann has also brought Chung criticism.
Last week, KFA sacked coach Klinsmann after he failed to help South Korea win the Asian Cup this year. The team lost 0-2 to Jordan in the semifinal.
The KFA noted that he has failed to display managerial capability and leadership in areas ranging from tactics to personnel management, which culminated in a scandalous bust-up between Son Heung-min and Lee Kang-in right ahead of the semifinal. Klinsmann's work attitude was also questioned, as he regularly worked from abroad instead of being in South Korea.
With Klinsmann's contract still valid until 2026, KFA must pay him and his coaching staff $7.5 million in compensation, which riled public opinion in South Korea. The media and fans have questioned why Chung and KFA agreed to pay Klinsmann such a high salary.
Over the past few days, large numbers of demonstrators have gathered in front of KFA headquarters to request Chung's resignation.
"The players' honor was harmed because the KFA blamed the defeat (against Jordan) on a quarrel between Son Heung-min and Lee Kang-in to avoid scathing criticism towards the association," read a statement the Public Welfare Committee released upon filing additional charges of defamation against Chung, coach Klinsmann and KFA vice chairman Kim Jung-bae.