Mette Frederiksen reiterated that the semi-autonomous Danish territory in the Arctic is not for sale.
Ms Frederiksen, who was visiting the world's largest island to meet premier Kim Kielsen, said: "Greenland is not Danish. Greenland is Greenlandic.
"I persistently hope that this is not something that is seriously meant."
Ms Frederiksen said that the Arctic, with resources that Russia and others could exploit for commercial gain, "is becoming increasingly important to the entire world community".
Mr Trump is expected to visit Denmark in early September as part of a trip to Europe.
Mr Trump said the idea of buying Greenland from Denmark has been discussed within his administration because of the strategic benefits for the US.
He also suggested that the semi-autonomous territory was a financial burden to Denmark.
Surprise and confusion greeted a Wall Street Journal report last Thursday that Mr Trump has been raising the subject of buying Greenland in recent weeks.
Officials in Greenland have said it is not for sale, and Mr Trump allowed on Sunday that it is not a priority of his administration.
"It's just something we've talked about," Mr Trump told reporters when asked about the idea.
"Denmark essentially owns it. We're very good allies with Denmark.
"We've protected Denmark like we protect large portions of the world, so the concept came up."
The US military has operated for decades from Thule Air Base in Greenland, which is situated between the Atlantic and Arctic oceans.
The northern-most US base is part of the military's global network of radars and other sensors to provide ballistic missile warning and space surveillance.
"Strategically it's interesting and we'd be interested, but we'll talk to them a little bit. It's not number one on the burner, I can tell you that," the president said.
Mr Trump, who made a fortune in the New York property market and owns or licenses properties around the world, appeared to cast the idea from the perspective of a developer.
"Essentially, it's a large real estate deal. A lot of things can be done.
"It's hurting Denmark very badly, because they're losing almost 700 million dollars (£577 million) a year carrying it. So they carry it at a great loss," he said.
White House economic adviser Larry Kudlow, appearing on Fox News Sunday, said Greenland was "a strategic place" with "a lot of valuable minerals".
Mr Trump is expected to visit Denmark in September as part of a trip to Europe.