South Korea's President Moon Jae-in is another fan, and has suggested Trump should get the Nobel Peace Prize. A raft of Republicans have begun a campaign for just that.
The Nobel Peace Prize, one of five Nobel awards generally given out annually for over 100 years, goes to whoever "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."
There's a strong precedent for giving the prize to leaders who have worked on nuclear disarmament or peace deals.
In 2017, the award went to the relatively unknown International Campaign to Abolish Nuclear Weapons for "its work to draw attention to the catastrophic humanitarian consequences of any use of nuclear weapons and for its ground-breaking efforts to achieve a treaty-based prohibition of such weapons."
In 2009, when former President Barack Obama had been in office for less than one year, he got the peace prize "for his extraordinary efforts to strengthen international diplomacy and cooperation between peoples."
"I do not feel that I deserve to be in the company of so many of the transformative figures who've been honoured by this prize," said Obama in accepting the award.
With Trump taking a new approach to North Korea, albeit an outwardly militaristic and threatening one, he has been credited with creating the conditions necessary to bring Kim Jong Un to the table.
But will the Norwegian Nobel Committee, five members appointed by Norway's parliament, confer Trump such an honour?
Trump made history by becoming the first US president to agree to meet with a North Korean leader, giving some credence to his "all options on the table" approach to Pyongyang.
All the signs from the inter-Korean summits and Kim's talks with China point to a positive, real peace push — but no real work has been done yet.
None of North Korea's nuclear infrastructure has been dismantled. No agreements on how and when the nuclear infrastructure would go have even been reached.
So far, the talk and atmosphere in the Koreas have become peaceful, but the problems remain.
Meanwhile, Trump has emerged as a sceptic of the Iran deal, another nuclear nonproliferation push, and could withdraw the US from it.
Trump is reportedly on the verge of exiting Iran deal, a move European governments have warned him against.
He could also be hampered by his support for acknowledging Jerusalem as the capital of Israel. Even though it is a long-held US position, the stance has been seen as aggravating tensions in the Middle East.
The Nobel Peace Prize is announced on December 10. That gives the committee plenty of time to see whether Trump makes the grade. The prize carries a cash award of about $350,000.Receive a single WhatsApp message every morning with all our latest news: Sign up here.