If Seoul does decide to send a special envoy to the North, local analysts say the presidential Chief of Staff Im Jong-seok, Unification Minister Cho Myoung-gyon or National Intelligence Service (NIS) Director Suh Hoon - all of whom accompanied Moon when he received the North Korean delegation at the Blue House last Saturday - are possible options.
North Korea's band of all-female supporters was unable to inspire the historic joint Korean women's ice hockey team as they were dumped out of the Pyeongchang Olympics with an 8-0 defeat to Sweden on Monday.
Kim Yo-jong, the younger sister of North Korean leader Kim Jong-un, delivered her brother's letter to President Moon Jae-in, which includes an invitation to Pyongyang at an early date.
In a meeting with the South Korean president on Thursday, Pence said the United States will continue to put maximum pressure on the North until the reclusive state comes to the dialogue table to discuss its "permanent" and "irreversible" denuclearization.
With the Winter Olympics taking place in South Korea, a rare friendliness has been seen between estranged neighbors North and South Korea.
"The North Koreans should understand that for a summit or any kind of serious talks to occur, Moon needs to be able to take something to Washington - something that addresses denuclearisation", he said.
Pence has meant to use his trip to the Olympics to caution the South against "falling for" the North's overtures, which in the past have been used as stall tactics to allow for continued development of its nuclear program.
Even Japanese Prime Minister Shinzo Abe, who has shared the American skepticism of warming North-South relations and pressed Moon against falling for the North's "smile diplomacy", greeted Kim Yong Nam.
But instead of broadcasting the morning event live, North Korean television aired an edited version later in the day, giving it a somewhat lower profile than expected. However, some powers, instead of extending them a helping hand in normalising their ties, are trying to spoil the atmosphere which is no service to the noble objective of restoration of much needed peace and tranquillity in the Korean peninsula.
Mr Moon could find himself in a delicate diplomatic position in the North Korean bid.
"All eyes are focused on Kim Yong Nam and Kim Yo Jong. if she would invite President Moon to Pyongyang", he told The Straits Times.
It would be the first summit in more than a decade between Korean leaders.
Pence, Kim Yo-jong, and other world leaders attended the opening ceremony in Pyeongchang, just 80 km (50 miles) from the heavily fortified border between North and South Korea.
The two Koreas have worked together to send a joint team to major global sports events only twice before - both in 1991, for the world table tennis championships in Japan and for soccer's World Youth Championship in Portugal. For his part, Abe said that Japan and the USA had "confirmed... that we can never accept a nuclear-armed North Korea".