Citing sources in the Danish government and military, and also among European allies, DR says blood supplies were also brought in to treat the wounded in the event of fighting.
The Financial Times newspaper said two European officials later confirmed the report. The Danish defence ministry told the BBC it "has no comment".
A senior Danish military official, speaking anonymously, told the BBC "only a limited number of people would have been aware of the operation for security reasons".
Both the US and Denmark are Nato members, and the issue of Greenland - a semi-autonomous part of Denmark - has deeply divided Washington and its European allies.
Trump has repeatedly said he wanted to annex Greenland during his second presidential term. Greenland's leader and Denmark have repeatedly rejected his demands to acquire the island.
