Sir Keir Starmer will host his Danish counterpart for a working dinner in Downing Street on Tuesday evening.
The UK Prime Minister and Denmark’s premier Mette Frederiksen are expected to discuss European security as well as the issue of migration at the meeting.
The dinner comes amid a diplomatic row between Denmark and the US over Donald Trump’s claims that he wants to acquire Greenland.
The US president has not ruled out sending US troops to seize Greenland.
Downing Street would not be drawn over whether Britain would support the US or Denmark in a dispute over the territory when asked by journalists on Monday.
The Prime Minister’s official spokesman said he was “not going to get into hypothetical situations”, but that the long-standing position on Denmark and Greenland is “well understood”.
Ms Frederiksen has called for a “collective and robust response” within the EU should the president press ahead with his threats to take over the territory.
Sir Keir has insisted that Britain can work with both the new administration in Washington and its European partners without choosing between them.
Speaking ahead of a meeting with the EU’s 27 leaders in Brussels on Monday, he said it was not an “either-or” decision to both keep Mr Trump onside and seek closer ties with the bloc.
As well as the issue of Greenland, the looming prospect of a trade war between the EU and US largely overshadowed the Prime Minister’s trip to Belgium.
Comments from Mr Trump overnight into Monday suggested that he was poised to expand his tariff regime to both the UK and Brussels, but that he thinks a deal can be done with Britain.
He later agreed to a 30-day pause on his tariff threats against Mexico and Canada as America’s two largest trading partners took steps to appease his concerns about border security and drug trafficking.
Earlier on Monday, Number 10 said the Prime Minister trusted Mr Trump and pointed to “a really constructive early set of conversations” between the two men.
“We’ve got a fair and balanced trading relationship which benefits both sides of the Atlantic,” Sir Keir’s spokesman said.
“It’s worth around £300 billion and we are each other’s single largest investors, with £1.2 trillion invested in each other’s economies.”
