The Korea Football Association's national team committee met a week on from the 2-0 defeat to Jordan in the semi-finals and with Klinsmann under huge pressure.
The committee is not a decision-making body but will make its recommendation to the KFA's executive board, which will make a final ruling on the 59-year-old German's fate.
A smattering of protesters gathered outside KFA headquarters in Seoul, demanding Klinsmann's removal after just less than a year in the post.
"We've reached a consensus that Klinsmann cannot exercise his leadership as national team head coach for various reasons and that a change of leadership is necessary," Hwangbo Kwan of the committee said.
After a three-hour meeting, Hwangbo said the committee had decided Klinsmann's "tactical preparation fell short" during the team's disappointing Asian Cup campaign in Qatar.
He added: "Klinsmann said there was discord among squad members and it affected their performance (in the Jordan match)."
Klinsmann attended the meeting on a video conference from his home in the United States, Yonhap news agency reported.
"There were opinions that Klinsmann failed to show his resolve to find new talent and that he failed to grasp internal conflict or mood among squad members in management," said Hwangbo.
"There were also reviews that he is appearing to ignore the Korean public for his short stays in South Korea and that he had lost trust from them," he added.
Yonhap previously reported, citing unnamed sources, that the KFA would consider a temporary appointment for next month's World Cup qualifiers against Thailand if Klinsmann were to be sacked.
Klinsmann, who has never won over South Korean fans or media, had promised to deliver the country's first Asian title in 64 years.
He has refused to resign despite fierce pressure and said he will remain living in the United States, despite demands from South Korean fans and media for him to move there.
Bust-up
The South Korean team have been in the eye of a storm.
On Wednesday came revelations about a bust-up between players that left Son Heung-min with an injured finger on the eve of the Jordan game in Qatar.
Paris Saint-Germain's Lee Kang-in on Wednesday issued an apology after Yonhap said the 22-year-old had tried to punch skipper and Tottenham star Son.
Lee's representatives have denied there was a punch.
The fracas was reportedly triggered by younger players -- including Lee -- rushing through their dinner so they could leave early and play table tennis.
This angered some of the older players, including Son, who wanted to honour longstanding tradition that the pre-game dinner be a team bonding experience, triggering the brawl.
Lee and Son both played in the Jordan defeat, the latter with two of his fingers strapped together.
He had the same dressing on his fingers when he came on at the weekend in Tottenham's 2-1 win over Brighton.
The incident has fuelled calls for Klinsmann to be sacked, with some saying it was more evidence of his weak management.