The Nobel Peace Prize is awarded to someone "who shall have done the most or the best work for fraternity between nations, the abolition or reduction of standing armies and for the holding and promotion of peace congresses", according to the prize's website.
Norwegian Progress Party leaders nominated the US president a day after the summit ended. It is unclear whether he was nominated for this year's prize.
The Hill reports that it was two members of Norway's right-wing Progress Party, Christian Tybring-Gjedde and Per-Willy Amundsen, who made the nomination.
A few suggested a less "mainstream" option for the next Nobel Prize victor, recalling Dennis Rodman's efforts in establishing the dialogue between the U.S. and North Korea.
United States believes North Korea disarmament to come in 30 months
He met Kim again in May when Trump said he was withdrawing from the planned summit with Kim - a decision Trump quickly reversed. The presentation bemused those of us packed into the press hall - we thought at first it was North Korean propaganda.
Trump himself has mused about earning the Nobel saying "everyone thinks so, but I would never say it", when asked about the possibility of the prize last month. So while Trump and Kim could be among the 330 nominees for 2018, an award linked to North Korea may be more likely in 2019.
During the summit, Trump and Kim signed a brief document committing the U.S.to unspecified security guarantees for North Korea in exchange for the denuclearization of the Korean Peninsula.
Former President Barack Obama earned the prize, as did Jimmy Carter, Theodore Roosevelt and Woodrow Wilson. North Korea also agreed to return the remains of American military personnel killed in that country during the Korean War from 1950 to 1953.
Trump has been cited as a possible nominee since Kim ended a series of provocative threats and missile tests a year ago.