The Dutchman has already steered South Korea to their sixth consecutive World Cup finals in Germany but a string of lacklustre performances has sparked calls for him to step down from the media and fans.
'The KFA's technical committee will very shortly discuss at length the current problems with the team' You Young-cheul media director for the Korea Football Association (KFA) said by telephone.
'It will then decide on the best course of action to ensure the team has the best preparation ahead of next year's World Cup. Once a decision has been reached we will make a public announcement' he added.
South Korea's Yonhap news agency quoted a senior KFA official as saying the committee could meet as early as Friday.
'All options including whether to dismiss Bonfrere will be discussed at the meeting' Yonhap quoted the official as saying.
Bonfrere told a media conference following the defeat to group winners Saudi he was still confident South Korea would perform well at next year's World Cup finals and pleaded for more time to work with the players.
But South Korean newspapers clamoured for his resignation criticising his team selections tactics and inability to communicate with players.
'Bonfrere we don't trust you now' said the Chosun Ilbo in an editorial claiming Bonfrere lacked the leadership and tactical flexibility needed for the job.
'Another collapse for Bonfrere - our patience is at an end' screamed the Joongang Ilbo.
Despite pitching in foreign-based players such as Ahn Jung-hwan Cha Du-ri and Lee Young-pyo Bonfrere had failed yet again to prove himself as a manager the newspaper said.
Criticism of Bonfrere's leadership has grown since South Korea finished last behind China North Korea and Japan in the East Asian Championship earlier this month.
A survey conducted by Internet portal naver.com following the tournament said 95 percent of respondents wanted Bonfrere to step down. The KFA warned at the time it would not ignore calls for his dismissal forever.
Bonfrere was a surprise replacement for Humberto Coelho who stepped down in April last year after a humiliating 0-0 draw with the Maldives in an Asian World Cup qualifier.