The famous cliff from 2014 hit-TV drama "My Love from the Star" has been temporarily closed to the public over safety concerns since April 22.
According to the Incheon Metropolitan City, the cliff in Songdo was graded worrisome D and E in its latest safety examination.
Experts have reportedly warned that the cliff face was unstable and could result in deadly rock falls due to having been previously used as a quarry up to 1994.
However, the city is known to have made exceptions for mass Chinese tour groups.
The Incheon Tourism Organisation said, "On occasions when the tourists make a group request through their travel agency, we have allowed short visits arranged in a way so that they were not too near the hazardous parts."
The Incheon city government plans to conduct meetings with relevant authorities on Monday to bolster safety measures and reopen the area as quickly as possible.
It also intends to brainstorm ways to transform the mountain on which the cliff is located into a distinguished hallyu theme park.
Building a cafe in the theme of "My Love from the Star" and a place where tourists can make wishes with "binyeo," the traditional Korean hairpin featured in the TV drama, are a few of the ideas that are under review. Offering rides in old-style Korean sedan chair is also being considered.
Starring actors Jun Ji-hyun and Kim Soo-hyun, "My Love from the Star" was a phenomenal success in 2014, both domestically and abroad.
The Songdo rock mountain is affectionately nicknamed the Cheon-Do cliff by drama fans, as it is where the lead female character Cheon Song-yi was rescued by her male counterpart Do Min-joon from a near-death experience.