The two burial sites in Jutland are highly controversial - one is near a bathing lake and the other not far from a source of drinking water.
The new Agriculture Minister, Rasmus Prehn, said that he supported the idea of exhuming the mink and incinerating them. But that would require the environmental protection agency's approval, he added.
His predecessor Mogens Jensen resigned last week in the furore over the government's legal basis for the cull, as more than 10,000 tonnes of dead mink were hastily buried.
About 11 million mink have been culled so far.
The government has admitted that the cull was mishandled. The grisly mass burial got even more macabre when there were reports of buried mink resurfacing because of the nitrogen and phosphorus gases produced by their decay.
Denmark has about 1,100 mink farms - and so far no compensation deal has been decided.
As we reported earlier, all minks with coronavirus have been culled in Denmark. It was noted that 284 mink farms were infected with Covid-19 and 25 mink farms were still under suspicion.
The killed minks have begun resurfacing from their graves. Newspapers have referred to them as the "zombie mink".