The world's largest island has been in the international spotlight in recent weeks after President Donald Trump repeatedly said he wants the US to acquire Greenland.
He has not ruled out out military force and economic coercion to gain control.
European Union Military Committee chairman Robert Brieger said Greenland is of great importance from a geopolitical and security policy perspective and said an EU deployment was worth considering.
"That would be a strong signal and could contribute to stability in the region," the Austrian general said in an interview with the German Sunday newspaper Welt am Sonntag.
"It would make perfect sense not only to station US forces in Greenland as before, but also to consider stationing EU soldiers there."
He noted there are extensive raw material deposits there, and important transport routes for international trade also pass through it.
"With the increasing melting of the ice as a result of climate change, however, this also creates a certain potential for tension with Russia and possibly China," he added.
Greenland is largely autonomous, but officially part of the Danish kingdom.
Trump had a fiery phone conversation with Denmark's Prime Minister Mette Frederiksen last week.
She insisted the island was not for sale and it was up to Greenlanders to decide their future.
Some Greenlanders are pushing for independence from Denmark.
"Trump is the president of a great power that is also a member of the United Nations," Brieger said.
"I therefore assume that he respects the inviolability of borders as laid down in the UN Charter."
Trump's son Donald Trump Jr caused a stir when he flew to the capital Nuuk earlier this month for a brief visit.
24°C