"President Trump should win the Nobel Peace Prize. What we need is only peace," Mr Moon told a meeting of senior secretaries, according to a presidential Blue House official who briefed media.
Mr Moon and North Korean leader Kim Jong-un on Friday pledged at a summit to end hostilities between their countries and work toward the "complete denuclearisation" of the Korean peninsula.
The Trump administration has led a global effort to impose stricter sanctions on North Korea, with the US president also exchanging bellicose threats with Mr Kim in the past year over North Korea's development of nuclear missiles capable of reaching the United States.Mr Trump is preparing for his own summit with Mr Kim, which he said would take place in the next three to four weeks.
In January, Mr Moon said Mr Trump "deserves big credit for bringing about the inter-Korean talks. It could be a resulting work of the US-led sanctions and pressure".
Mr Moon responded by saying Mr Trump should get it. Mr Trump's predecessor Barack Obama won the 2009 Nobel Peace Prize just months into his presidency, an award many thought was premature, given that he had little to show for his peace efforts beyond rhetoric.
Even Mr Obama said he was surprised and by the time he collected the prize in Oslo at the end of that year, he had ordered the tripling of US troops in Afghanistan.
Mr Moon's Nobel Prize comment came in response to a congratulatory message from Lee Hee-ho, the widow of late South Korean president Kim Dae-jung, in which she said Mr Moon deserved to win the prize, the Blue House official said.