Suddenly, Greenland is saying that it would not mind housing the weapons if to do so would help the cause of international detente. Given the geographical position of the world's largest island - midway between North America and Russia, the proposal seems perfectly apt.
The offer has been made directly by Lars Emil Johansen, the Premier of Greenland. Mr Johansen leads the centre-left coalition that governs Greenland under its partial home-rule relationship with Denmark.
Greenland "doesn't want to be a dumping ground, but we would like to make our contribution to the world peace," Mr Johansen told the Danish newspaper, Jyllands Posten this weekend. Weapons from either side in the Cold War, America and the Soviet Union, would be welcome, he added.
However, it is likely that Mr Johansen may have to smooth some ruffled feathers in Denmark first before the offer can be made formally to Moscow and Washington. Denmark still has responsibility for Greenland's foreign and defence policy.
The Danish Foreign Minister, Niels Helveg Petersen, was said this weekend to have been "very surprised" by the proposal.
Ties between Denmark and its Arctic dependency have long between tense. Greenland, which has a population of only 57,000 huddled mostly along its southern coastline, has made no secret of its long-term desire to become a fully sovereign nation. It remains heavily dependent on Danish subsidies, however.
Moreover, the proposal is likely to reawaken some sensitive memories in Denmark.
During the Cold War, Greenland secretly provided storage space for American nuclear warheads, even though Denmark had voted in 1957 to ban all nuclear materials from its soil.
When the secret was revealed, it turned out that very few even in the highest levels of Danish government had been aware of it.
The notion of using Greenland as a garage for the warheads first surfaced in a report published in the US in February by the Rand Institute. The Institute this weekend welcomed Mr Johansen's offer.
"It is great news for the whole world that the Greenland Home Rule [government] is willing to make an initiative," a Rand spokesman said.