Mike Pompeo is due to arrive in Denmark around 10am to meet with Prime Minister Mette Frederiksen.
He is then expected to hold talks with his Danish counterpart Jeppe Kofod at noon, when they will be joined by foreign affairs representatives for Greenland and the Faroe Islands, also a Danish autonomous territory.
In Kofod's words, Denmark considers the US its “absolutely closest ally” and has contributed troops to NATO missions in Afghanistan, Iraq and Libya.
But relations hit some turbulence in August 2019 when Trump floated the idea of the US buying Greenland, an Arctic territory covering over two million square kilometres.
Frederiksen called the proposal “absurd”, leading Trump to cancel a planned visit to Copenhagen over the “nasty” tone of the response.
While the offer was the subject of some ridicule, analysts say it is also indicative of the US' renewed strategic interest in the Arctic region, which had subsided somewhat after the end of the Cold War.
A few phone calls between the countries have since eased the tensions, and Greenland officials say they want to put the affair behind them.
“What we said in the past and what we do today are two different things. And what matters is what we do and what we say today,” Greenland foreign affairs representative Steen Lynge told reporters on Tuesday.
The US reopened a consulate in Greenland's capital Nuuk last month, with approval from Copenhagen, and provided a $12.1 million aid package in April.
But there is another bone of contention: the Nord Stream 2 gas pipeline being built between Russia and Germany.
The US strongly opposes the pipeline, which runs through Danish waters, saying it risks increasing the dependence of NATO countries on Russian gas.
It imposed sanctions on companies working on the project late last year — a move strongly opposed by the European Union.
Denmark was the last country to approve the pipeline, holding up the unveiling by several months, before finally providing the green light in October 2019.
Copenhagen denied any foreign pressure over the issue, but a diplomatic source told AFP the small Nordic country has faced great difficulty in balancing the interests of its two main allies, the US and Germany.