Frederiksen said this after a visit to Keir Starmer on Thursday, at the British Prime Minister's country residence, Chequers.
"We have begun work with the US government, and we are in the process of clarifying exactly how it will proceed in the coming weeks," Frederiksen said, according to the Ritzau news agency.
Rutte lacks mandate
She emphasized again that only Denmark and Greenland have the right to negotiate about Greenland, after Wednesday's US reversal on the issue following a meeting between President Donald Trump and Dutch Prime Minister Mark Rutte.
He does not have a mandate to negotiate on behalf of Denmark or Greenland, Frederiksen told DR earlier on Thursday.
"We must find a path that respects both international law and sovereignty," she said in the interview.
She also emphasized that Denmark's red line of not giving up any sovereignty remains firm.
“Fully understood”
The interview followed a written statement that morning in which Frederiksen stated that the Danish and Greenlandic governments were kept informed about the conversation between Rutte and Trump in Davos.
The question of Danish and Greenlandic sovereignty has not been raised, she said.
"NATO fully agrees with the position of the Kingdom of Denmark. We can negotiate on everything political: security, investments and the economy," she said.
"But we cannot negotiate our sovereignty."
She stressed that Denmark wants to have a continued, constructive dialogue with allies on how security in the Arctic can be strengthened, including the US's so-called Gold Dome (a missile defense system).
"Provided that it is done with respect for our territorial sovereignty."
