I have not seen any official Norwegian stance on this.  Nor any debate in the public domain after a quick google search (but try to search 'Hans Ø' in 'any language' - and you'll find many Danish pages).
I suspect that most Norwegians will have some sympathy for the Danish position since Greenland (along with Iceland and the Faroes) were Norwegian possessions from viking times until the union with and later integration into Denmark.  Upon Norwegian independence from Denmark, the overseas possessions remained with Denmark.  Iceland has obviously later become independent, while Greenland and the Faroes have a large degree of autonomy.
As observed in comments above, this resource really belongs to the indiginous population.
AFAIK, Denmark and Canada are the only naval powers in that area - unless the US wants to meddle (?).