"Currently we are working on the next steps to make sure that indeed we collectively protect what is at stake," Rutte told journalists during a visit to Croatia.
Trump has rocked the 32-nation alliance by refusing to rule out military force to seize the autonomous territory of fellow NATO member Denmark.
The US leader has used a need to increase security in the Arctic region in the face of China and Russia as a key justification for why Washington needs to control the island.
"All allies agree on the importance of the Arctic and Arctic security, because we know that with sea lanes opening up there is a risk that the Russians and the Chinese will be more active," Rutte said.
"Currently we are discussing the next step to that, how to make sure that we give practical follow up on those discussions," he said.
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.
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