During the meeting, Moon would brief Trump on his recent summit meeting with North Korean leader Kim Jong-un.
The warnings from North Korea are a reminder that it will seek to project an image of strength for domestic and overseas audiences, even as the country says it's moving forward with rapprochement with the United States and South Korea.
North Korea has long viewed the 28,500-strong USA force as a threat to its regime, and is widely expected to seek concessions in return for the dismantling of its nuclear program.
North Korean Leader Kim Jong Un (L) and South KoreanPresident Moon Jae-in (R) shake hands over the military demarcation line upon meeting for the Inter-Korean Summit on April 27, 2018 in Panmunjom, South Korea.
But America will probably still insist Mr Trump's tough stance has been decisive considering just past year Mr Kim was launching long-range missiles at a record pace.
"I had an in-depth discussion with John Bolton, assistant to the president for national security affairs, to explore ways to make the upcoming North-Washington summit successful", said Chung upon arrival in Seoul on Saturday.
"It is the arrogance of outsiders to suggest that the North Koreans are debating or talking to us because of either Trump-ian pressure on the right or [South Korean President] Moon's liberal engagement on the left".
Asked whether he would use the possibility of reducing the size of the USFK as a bargaining chip in his highly anticipated meeting with Kim, he replied, "Not really, not at this moment, certainly not". According to Trump, "good things are happening, but only time will tell!"
North Korea set its clocks forward by 30 minutes on Friday to match South Korean time zone. On the outcome of his summit with Kim, he remarked, "We'll see what happens".
"I have no doubt their hope is to divide us from our allies in South Korea, to ease some of the sanctions, to ease the pressure coming from China so that they are not so isolated in the world", he said.
Trump hailed Friday's Moon-Kim meeting, declaring "TO END!" on Twitter.
Experts say other possible venues could be Singapore or Ulaanbaatar.
North Korea has denied claims that US-led sanctions are what encouraged it to seek worldwide peace talks, and experts say it was arrogance to ever think that was the case.