Moon Jae-in’s comment came after a historic summit on Friday in which he met North Korean leader Kim Jong Un.
“President Trump should win the Nobel Peace Prize. What we need is only peace,” Mr Moon told a meeting of senior secretaries, according to an official who briefed media.
During the first inter-Korean summit in more than a decade, both leaders stepped into North and South Korea before agreeing to a “complete denuclearisation” of their peninsula.
Mr Trump is preparing for his own summit with North Korea, suggesting that it might be held in a truce village that straddles the border separating the two Koreas.
“Numerous countries are being considered for the MEETING, but would Peace House/Freedom House, on the Border of North & South Korea, be a more Representative, Important and Lasting site than a third party country? Just asking!” the US President tweeted.
In floating the idea of a Trump Nobel, Mr Moon was responding to a comment by Lee Hee-ho, the widow of late South Korean President Kim Dae-jung.
She said Mr Moon deserved to win the prize in recognition of his peace efforts, leading him to say Mr Trump should get it.
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”.
During Monday’s meeting, Mr Moon called for a joint study with the North to identify economic projects that could be resumed without violating international sanctions imposed on North Korea for its nuclear weapons and ballistic missile programmes.
“The study is to set in motion the programmes that are not subject to sanctions, while exploring what the two Koreas could do when the sanctions are lifted in the future,” the official quoted Mr Moon as saying.
The Trump administration has been leading a global effort to impose tougher sanctions on North Korea.
US Secretary of State Mike Pompeo said on Sunday that Mr Trump would maintain a “pressure campaign” of sanctions on North Korea until the nuclear weapon programme is demolished.
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Late Saturday, Mr Trump told Mr Moon in a phone call that he was pleased the leaders of the two Koreas reaffirmed the goal of complete denuclearisation.
The White House confirmed in March that a US-North Korea summit would take place. Mr Trump said last week he is weighing up “three or four dates” and “five locations” for the talks.