Denmark itself is a pretty valuable strategic asset. What with controlling the seaways into the Baltic. If Greenland is valuable, then Denmark would likely be guaranteed to own it. In the same way, that Denmark has remained independent.
During the Second Schleswig War in 1864, the King of Denmark offered Otto von Bismarck thrice that Denmark - instead of relinquishing Schleswig - would join the German Confederation - which Bismarck would later turn into the German Empire.
All three times, Bismarck rejected the offer for two primary reasons: 1) He did not believe Danes would join a pan-German state and 2) (more importantly) the other great powers would have a big problem with Denmark being German.
In the same fashion, the fight over Greenland would lead to the compromise solution that Greenland remain none of the great/super powers. The US would never accept it falling into Russian hands, but they could accept Denmark keeping it.