Wikipedia has an uncited statement that William Seward advocated the USA purchase of Greenland in 1867, though it doesn't seem this proposal led to negotiations with Denmark.
1. Is this true?
There was apparently some interest.
However, in the 1860s, Denmark's "colony" on Greenland was considered rather to occupy certainly the smaller part of Greenland. Norway harbored some claims to Greenland through the 1800s as well.
A century earlier, in the 1770s Denmark and the Netherlands were squabbling about it some. But later Norways' claim over Greenland was an issue resulted from the post-Napoleonic Wars Treaty of Kiel of 1814, where Denmark released all claim over the Kingdom of Norway, EXCEPT (in Article IV) to Greenland, Iceland and the Faroe Islands....
There was some discontent over that Treaty by Norway apparently...
Besides Greenland, the United States, and Secretary of State Seward, was in negotiation with Denmark from 1865, relative to acquiring its West Indian Virgin islands...
The USA moved to procure the islands finally in 1916-17.
2. What value did the Seward see in Greenland in 1867?
The situation and resources of Greenland were laid out for the US Government in this 1868 report for Secretary of State Seward...
3. How does this proposal relate to the USA purchase of Alaska from Russia in 1867?
Former Secretary of the Treasury Robert J. Walker personally approved of the administration's official interest in Greenland for strategic purposes, alongside Alaska, for strategic purposes. Writing Secretary of State Seward on April 24, 1868, he opined...
....
The USA was at that time involved in the "Alabama Claims" dispute with Great Britain, which was settled in 1872.
4. What was the value seen in Alaska in 1867?
In December, 1866, President Johnson's annual message noted his negotiations with Russia, relative to procuring Alaska and the purpose therefore...
The oil came later. Was it just the whaling fleet and wanting to get Russia out of North America?
The boundary between "Russian America" and "British Canada" had been a sticking point. The USA purchased Russia's American dominion and worked out a treaty with Britain relative to the boundaries and rights later.
The American purchase removed Russia from the dispute. The British concerns were then directed toward the United States, and there was an international arbitration relative to the Behring Sea in 1893:
As outlined in this Canadian publication from the British perspective...
Alaska, like Greenland, Venezuela, etc., was otherwise always included under the umbrella of the Monroe Doctrine generally, which, according to Joshua Leavitt from 1863, was in effect whenever the Europeans attempt to institute a "balance of power" system/struggle over any part of the Western Hemisphere, which the United States views negatively....
For example, by mid-1865 the USA was able to pay attention to the French intervention in Mexico, and Secretary Seward communicated that the United States opposed their idea of establishing a permanent Government there...
After the French withdrew, Emperor Maximillian's government in Mexico collapsed, etc. in June, 1867.
Reminder: we are discussing American foreign policy in the 19th century. Discussion about 21st century Greenland issues is prohibited by forum rules.
The settlement of much of the above issues came in the early 20th Century, the USA fully acceded to and indorsed Denmark's singular claims to the entirety of Greenland in 1916, along with finally securing the Virgin Islands.
However, any residual "preemptive" rights claims to Greenland by Europeans, should Denmark alienate its sovereignty, the USA does not recognize, as noted in this 1940 report by Secretary of State Hull:
history.state.gov 3.0 shell
history.state.gov