Moon had said "let's create conditions to make it happen", the official said, an indication that Moon was likely to accept the invitation.
Analysts say the North's decision to shows an ambition to break out from diplomatic isolation and pressure by improving relations with the South, which it could use as a bridge for approaching the United States.
But they cautioned against any excessive optimism about her travel, saying that an improvement of inter-Korean relations would be limited without progress over the resolution of North Korea's nuclear standoff.
South Korean Prime Minister Lee Nak-yon on Sunday hosted a lunch for the high-ranking North Korean delegation, including Kim Jong-un's younger sister.
Still, the United States has a huge influence on talks of how to handle the North's threats of nuclear attacks.
"There is no daylight between the United States, the Republic of Korea and Japan on the need to continue to isolate North Korea economically and diplomatically until they abandon their nuclear and ballistic missile program", Vice President Mike Pence told reporters after a short visit here. President Moon and I reflected on that last night.
Kim Jong Un's sister, South's President Moon shake hands at Olympic opening
Mr Moon is eager to use Kim Yo Jong's presence at the games to restore regular communication with North Korea and eventually pull it into nuclear talks.
USA forces surround North Korea with a ring of warships, tanks, soldiers and missiles in the Pacific.
Moon joined Pence in the arena and sat next to him, turned around to greet Warmbier, according to a White House pool report.
On the same day, Moon and the North's delegation also jointly attended the opening match of the unified women's ice hockey team, which is comprised of athletes from the two Koreas.
Fred Warmbier accompanied Pence during his visit to South Korea.
Tensions between the two soared past year as Pyongyang launched intercontinental ballistic missiles capable of reaching the U.S. mainland and carried out by far its most powerful nuclear test to date.
Another Seoul-based expert said the decision to send a special envoy before holding the summit would help set up a table for dialogue between the U.S. and North Korea, which is the main agenda of the Moon administration.
The North's delegation to the Games also includes the country's ceremonial head of state as well as hundreds of female cheerleaders. Instead, Pence was criticized by North Korean media, accused of not respecting the "Olympic spirit".
"Sending a special envoy to the North will be a step toward finding out Kim Jong-un's true intentions behind the current overture", said Koh Yoo-hwan, a professor of North Korean studies at Dongguk University.