South Korea brought back Hong for a second spell in charge of the team in July, ending a five-month wait for a new coach after Klinsmann was sacked in February.
Hong oversaw two World Cup qualifiers in September, including a 0-0 draw with Palestine, during which fans jeered him to express displeasure at his appointment.
After Hong's hiring encountered backlash, Korea's sports ministry began an investigation into the operations of the KFA, which maintained that it never broke any rules.
Last week, Hong said his appointment was not the result of preferential treatment by the KFA, adding that he took the job after meeting its technical director, Lee Lim-saeng.
Hong's meeting with Lee was not a proper interview and Lee did not have the authority to recommend a coach, however, the sports ministry said on Wednesday, unveiling the interim results of its inquiry.
"(Lee) was involved in the process just because the KFA chairman and vice chairman, neither of whom have the authority to appoint the coach, delegated authority and ordered him to take follow-up steps," ministry official Choi Hyun-joon told reporters.
"The face-to-face interview process between Lee and Hong on July 5 was different from that of other foreign coach candidates.
"It is difficult to see it as a reasonable interview process, as there was no pre-interview questionnaire or an observer, but Lee had waited alone for a long time to conduct the interview late at night near his home, during which he asked Hong to take the coach position."
The KFA did not immediately respond to a request for comment.
South Korean media have said former Norwich City manager David Wagner, Canada coach Jesse Marsch and former Greece coach Gus Poyet were among the other candidates in the fray.
Despite its findings, the sports ministry stopped short of making the KFA scrap Hong's contract.
"We expect the KFA to review the situation and make its own decision from the perspective of public opinion and common sense," Choi added.
"Our audit did not find any evidence that illegal measures were taken in order to select Hong as coach, but I think that since the issue of appointing the national team coach is a big issue that the entire nation is interested in, the procedure and process should comply with the rules, be fair and meet public expectations as much as possible."
Final inquiry results are expected at the end of October.
The ministry added that the KFA also broke rules when hiring Hong's predecessor Klinsmann in 2023 and that it had not allowed the National Team Committee, an advisory body that recommends the national team's coaches, to function properly.
"The members of the committee had been excluded from the process from the beginning and were not able to participate in the candidate interview process," Choi said.
