In 1867, the United States entered negotiations with Denmark about buying overseas possessions. But what the US was actually interested in was some nice islands in the Caribbean. At the suggestion of the former Sec. Treasury Robert J. Walker, a strong proponent of American expansionism, Sec. State William H. Seward looked into whether Greenland and Iceland would would also be available as sort of a bonus, the ice already broken from the initial deal. Walker worked with the U.S. Coast Survey to write up a report which made wildly optimistic claims about how by possessing Greenland and Iceland, Canada would presumably decide to separate from Great Britain entirely and join the US:

Now, the acquisition of Greenland will flank British America for thousands of miles on the north and west, and greatly increase her inducements, peacefully and cheerfully, to become a part of the American Union.

More practically of course the report also spoke of how well suited they would be for telegraph lines across the oceans, and talked up the natural resources they could afford the United States. In the summary of the report, Walker touted both strongly:

[Iceland] has fields beautifully green, mountains clothed in purple heath, and the atmosphere is of astonishing purity." The lava in time becomes soil and pasture-land." Much of the heath can be made pasture-land. About onethird part of the males are farmers, the remainder are mainly occupied in the mines and fisheries. The population of Iceland is about 70,000, but in view of its pasture and arable lands, its valuable mines, its splendid fisheries, and its unsurpassed hydraulic power, it could, when fully developed, sustain population exceeding 1,000,000. It has been greatly neglected by Denmark. The Icelanders complain of this, and look forward with hope to association with the United States. It has numerous lakes, rivers, bays, estuaries, and fiords, with jL,, many good harbors. [...] It is misnamed Iceland, for, owing to the Gulf Stream, its climate is fine and almost temperate.

Greenland has in vast quantities whale, walrus, seal, and shark, cod, ivory-cod, salmon, salmon-trout, and herring; foxes, wolf, reindeer, bear, hare, myriads of birds, including the kiug duck, eider duck, dorskin, petrel, gull, brent, burgo master, goose, killiwoke, lolard, and sea swallow, &c, &c. Good coal is found on the western coast at various points, extending far north, most cheaply mined, and close to good harbors.

He goes on at length.

The whole idea was not well thought out though, and that was the reaction to it in Congress. During discussions of appropriations, when Rep. Cadwallader C. Washburn stood up to oppose the West Indies deal, he read from the report as well and lambasted the entire enterprise:

But are we to stop with the purchase of Alaska and St. Thomas? No, sir. I believe a treaty is now being negotiated with Denmark for the purchase of Greenland and Iceland. I have had placed upon my table since I began to speak to-day some pages of a document now printing at the Government Printing Office for the State Department, which shows that the purchase of Greenland is in contemplation.

The result was outright laughter from the House.

Not even the West Indies were popular though, so given that they were secondary in any case, the scuttling of the treaty ensured that none of this was going to happen. Few saw any benefit in any of this. Rep. Benjamin F. Butler decried the US wasting money on buy "the earthquakes in St. Thomas and ice-fields in Greenland". The government was already incredibly unstable in the wake of the impeachment of Andrew Johnson, and the Senate, after several years refusing to even vote on it, finally took the time to reject the treaty in 1870. To be sure, Denmark absolutely would have accepted the deal for the Indies, having the treaty having been ratified by them, and a plebiscite in the Danish West Indies endorsing it. Negotiations for Iceland and Greenland never got to the point where a real deal was on the table though, so we can only speculate on that. Although the Danish West Indies would eventually be bought several decades later, now the US Virgin Islands, the treaty was dead. It was clear that there was no sense in continuing attempts to purchase Greenland or Iceland, and doubly so with Seward having left his position in the State Department, so the matter was abandoned. The topic was of course revisited again in the 20th century, but I'll leave that story to someone else!

Sources

Dyer, Brainerd. "Robert J. Walker on Acquiring Greenland and Iceland." The Mississippi Valley Historical Review 27, no. 2 (1940): 263-66.

Gissurarson, Hannes Hólmsteinn. "Proposals to Sell, Annex or Evacuate Iceland, 1518–1868." Rannsóknir í félagsvísindum XVI. Erindi flutt á ráðstefnu (2015).

Peirce, B.M. A Report on the Resources of Iceland and Greenland. Government Printing Office, 1868.

Could you please cite the article or paper you read? I'm Icelandic and I had no idea about this and am interested to learn.