Asked at a security conference in Munich if Trump still wanted to own the Arctic island, Frederiksen said: "Unfortunately, I think the desire is the same."
Trump's designs on Greenland have caused tension to soar between the United States and Europe.
Last month, he backed down from his threats to seize the island, an autonomous territory of ally Denmark, after striking what he called a "framework" deal with NATO Secretary General Mark Rutte.
But relations have remained strained.
"Everybody asks us, do we think it's over? I mean, no, we don't think it's over," Frederiksen said, participating in a panel discussion on Arctic security.
Trump insists mineral-rich Greenland is vital for US and NATO security against Russia and China as superpowers jostle for strategic advantage.
Frederiksen and her Greenlandic counterpart, Jens-Frederik Nielsen, said the pressure on the island's people was "unacceptable".
But Nielsen said "some steps" had been taken "in the right direction".
A US-Denmark-Greenland working group has been established to discuss Washington's security concerns in the Arctic, but details have not been made public.
"We now have a working group, it's good. We will try to see if we can find a solution... But of course, there are red lines that will not be crossed. And we will stick to our strategy," Frederiksen said.
The remarks came after Frederiksen and Nielsen had a 15-minute meeting with US Secretary of State Marco Rubio on Friday on the sidelines of the security conference, which Frederiksen later described as "constructive".
Comments