However, administration officials noted that the United States and South Korea have been in talks on revamping the pact, also known as KORUS.
During his visit to hurricane-hit Houston in Texas over the weekend, Trump told reporters that he would be discussing the future of the KORUS FTA in the upcoming week, hinting that he would be looking for ways to pull out of the 5-year-old trade pact.
The free trade question comes at a sensitive time diplomatically, with the United States and South Korea working in tandem to counter aggression from North Korea through its development and testing of nuclear weapons and long-range missiles.
No final decision has been made and Mr Trump could remain in the agreement to see if changes are still possible, the newspaper reported, citing several people close to the process, whom it did not identify. "Withdrawing from KORUS would significantly disadvantage many successful US exporters, seriously harm many USA manufacturers and consumers, and badly undermine broader USA economic and strategic interests". However, a White House spokeswoman told the Post that discussions are ongoing, but there is nothing to be announced at this time.
However, it is thought that Trump's rhetoric about withdrawing from the trade deal may be a negotiation tactic, as he can not actually revoke the agreement without the approval of the U.S. Senate.
A South Korean trade ministry official said the government has been "thoroughly preparing for all possibilities" and would negotiate with Washington with an open attitude.
Neither the White House or the Office of U.S. Trade Representative confirmed or denied the possible move.
Mr Trump's push to revise the deal is part of his broader drive to tackle unfair trading practices and cut the USA trade deficit.
Trump on August 27 renewed his threat to scrap the North American Free Trade Agreement (NAFTA) between the United States, Canada and Mexico ahead of this week's second round of negotiations on rewriting the 23-year-old agreement. Mr Trump said last month that Canada and Mexico are being "difficult" and he will probably need to scrap the pact.
Critics argue pulling out of the deal could strain relations between the countries as they both try and mitigate how to deal with the threat of North Korea's nuclear weapons program.
Trump is weighing the issue at a perilous moment for the Korea peninsula.
But it remains unclear whether the administration would actually withdraw from the deal, and industry representatives who have lobbied the White House say the President's team has done little of the work - like a wide consultation with affected industries - needed before taking such a step.
Kim, like most economists, rejected Trump's assertion that KORUS was to blame for the United States' widening trade deficit with South Korea over the first years of the pact and demanded to know Trump's real motive in seeking a renegotiation, the Chamber memo said.