U.N. Secretary-General Ban Ki-moon has repeatedly said he is not interested in South Korean politics, but he is still the most favored among potential candidates for the 2017 presidential election.
In April, Ban said he wants to spend time taking care of his grandchildren after his retirement.
It remains unclear whether the U.N. chief can realize his simple dream as he could be at the center of South Korean politics in the coming years.
A latest poll showed that the former South Korean foreign minister received 21.1 percent of public support as a possible candidate for the presidential election.
The leaders of South Korea's ruling and opposition parties trailed far behind Ban, with 14.1 and 11.2 percent, respectively, according to the survey conducted by polling agency TNS Korea. The survey had a margin of error of plus or minus 3.1 percentage points.
The survey result came as Ban and South Korean President Park Geun-hye exchanged public messages in support of each other at the U.N.
Park has unveiled her commitment to making contributions to the sustainable development agenda and the U.N. climate change conference, the two major issues pushed by Ban.
Park also attended an informal working lunch Ban hosted to build momentum in leading up to the climate conference meant to produce a new legally binding deal cut the heat-trapping gases.
Meanwhile, Ban hosted a closed-door banquet in Park's honor at his official residence soon after Park arrived in New York for the U.N. General Assembly on Friday.
The two met each other on several occasions during the U.N.
sessions. In the session on South Korea's "Saemaeul Movement," or new community movement, Ban said he was moved as U.N. member states adopted and carried out the movement for the first time in the history of the U.N.
The initiative -- launched by Park's father, then-President Park Chung-hee, in the 1970s -- is credited with helping modernize the then-rural South Korean economy.
Ban also said the Saemaeul Movement spread in countries ranging from Asia to Africa "like a forest fire."
He also expressed gratitude to Park for sharing South Korea's development know-how with developing countries.
Park smiled and clapped her hands after Ban's speech and told him "thanks" in Korean.
Ban also vowed to assist in efforts to promote peace and the development of inter-Korean relations, a key agenda of Park.
The apparent rapport between the two leaders and Ban's active support of Park in the U.N. may rekindle the rumor of Ban's possible candidacy, despite his objection to getting involved in South Korea's domestic politics.
Ban's second five-year term at the U.N. is set to end at the end of 2016, a year before South Koreans go to the polls to elect a new president who will replace Park.
Park's single five-year term ends in early 2018, and by law, she cannot seek re-election. (Yonhap)