The Wall Street Journal, citing two unnamed advisers, reported late Thursday that Trump has, "with varying degrees of seriousness, repeatedly expressed interest" in buying the island in the North Atlantic.
Another prominent opposition member said the report indicates that Trump is "insane", while a member of the government bloc called it a "terrible idea". Avoiding an economic slump is critical to Trump's reelection hopes.
Pro-Brexit leaders are relying heavily on the traditionally close relationship with the United States, and Trump has sought to raise expectations.
Lewandowski has always been a lightning rod for criticism, but also unshakably loyal to Trump.
In today's money that would be worth roughly $1.3 billion (£1.07 billion).
This isn't the first time the president has expressed interest in foreign properties - he has said North Korea's "great beaches" would make ideal locations for condos.
According to the White House, the trip to Denmark follows a stop in Poland where the president and first lady will attend 80 anniversary commemorations of the start of World War II.
Trump also elaborated on his new push to consider building more mental institutions to prevent further mass shootings.
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"I like some of what Trump's been doing but I can't stand his mouth, and that was right after the whole grabbing the woman thing", Fabian said, referring to the release of the "Access Hollywood" tape in which Trump is heard describing women in vulgar terms.
He said: "We will be taking mentally deranged and risky people off of the streets so we won't have to worry so much about them". He's got a bigger problem than all of us. "There are seriously ill people and they're on the streets".
"New Hampshire should have been won last time, except we had a lot of people come in at the last moment, which was a rather unusual situation - thousands and thousands of people coming in from locations unknown, but I knew where their location was", he told reporters.
Mr. Trump's rally is expected to be held at the SNHU arena in Manchester at 7 p.m.
On Monday, Trump's hawkish foreign policy adviser John Bolton said in London that he wanted to see trade talks "move very quickly" after Brexit.
Mueller said his investigation did not find sufficient evidence to prove that Trump campaign officials conspired with Russian Federation, despite numerous contacts.
Trump also mentioned his general election loss in New Hampshire during the rally, telling those in the audience that it wasn't their fault.
Trump is due to visit Denmark next month, but it is not clear if the idea of purchasing Greenland will be on the agenda.
"(Trump) doesn't have an economic strategy that's created to win New Hampshire", Lacy said.