Diplomats at NATO say that some alliance members are floating ideas including possibly launching a new mission in the region.
But so far discussions are at an embryonic stage and there are no concrete proposals on the table, they say.
European leaders have thrown their weight behind Denmark as it seeks to fend off Trump’s desire for Greenland.
The foreign ministers of Denmark and Greenland are set to hold talks this week with US top diplomat Marco Rubio.
Danish Prime Minister Mette Frederiksen has warned that if Washington followed through with an armed attack on Greenland that it would spell the end of NATO.
Trump however has reacted by insisting he has made the alliance stronger by forcing European countries to up defence spending.
“I’m the one who SAVED NATO!!!” Trump posted online.