Last month, Trump, who is due to assume office on January 20, called it "an absolute necessity" for the United States to own Greenland. Greenland's Prime Minister Mute Egede said in response that the island was not for sale.
"To authorize the President to seek to enter into negotiations with the Kingdom of Denmark to secure the acquisition of Greenland by the United States," the draft document says.
The document may be referred to as "Make Greenland Great Again Act," it says.
If passed, the authorization would take effect on January 20, when Trump is set to officially assume office after his inauguration.
Greenland was a colony of Denmark until 1953. It remains part of the kingdom, but in 2009 it received autonomy with the ability to self-govern and make independent choices in domestic policy.