It's complicated.

When the Crimean War broke out, the Russian-American Company (RAC) was frantic with concern. The Russian naval presence in the Pacific was miniscule, and the defenses of Russian America were pitiful. At any time, the British or French might successfully attack New Archangel (Sitka) and if not seize the colony outright, then damage it so greatly as to make it worthless.

To avoid this circumstance, the RAC's head officers negotiated in London with officials from the Hudson Bay Company, and what they came up with was an informal truce. The RAC's holdings in Russian America would not be attacked, but the truce would not extend to sea. The British were interested in this truce both to protect the Hudson's Bay colonies from Russian raiders (a fear much inflated over the fact) and because they feared Russia might seek to turn Russian America over to the United States, something the British embassy in Washington had been instructed to specifically look out for.

Ironically, there was a movement afoot to do exactly that. Separated by vast distances from their managers in St. Petersburg, the officials within Russian America itself had plotted a false sale of company assets to an American shell corporation in order to protect the company from the war. The idea was that under the American flag, the RAC would be protected from British or French attack. This idea was pursued without any knowledge of the officials in St. Petersburg, and it petered out once word of the truce came back to Russian America and California.

The Crimean War turned disastrous for Russia, though it had some local successes (see John Grainger's The First Pacific War: Britain and Russia, 1854-56). Moreover, the fighting demonstrated Russia's Pacific vulnerability in the event of war.

Grand Duke Constantine, younger brother of Tsar Alexander II, commanded the Russian Navy, and became one of the leading advocates of the sale of Russian America. In 1857, he wrote: "we would do well to take advantage of the excess of money at the present time in the treasury of the United States of America and sell them our North American colonies."

Two years distant from the Crimean War, there was no thought among the higher-ups in the Russian Imperial government to selling Russian America to Great Britain. A sale to America, it was thought, would put pressure on "British Oregon" (the crown colony of British Columbia was not proclaimed until 1858) and avoid a confrontation with the United States, which appeared destined to take over all of North America, Constantine thought.

More than direct military conquest and takeover, Imperial officials feared a Texas-like scenario whereby settlers arriving in Russian America would grow to outnumber Russians and Creole Natives, then wrest control of Alaska from Russia. Worse than Americans, those settlers might be British.

In 1847, the Hudson Bay Company established Fort Yukon at the confluence of the Yukon and Porcupine rivers. Fort Yukon was well west of the 141st parallel, which had been set by 1825 treaty as the border between British Canada and Russian America. The Russians were aware of Fort Yukon ─ when, I'm not exactly sure, as an 1863 Russian map identifies its location exactly, but I'm not aware of earlier references.

In the late 1850s, gold was discovered in the Queen Charlotte Islands and then in the country of the Stikine River in northwestern British Columbia. The mouth of the Stikine is in Alaska, but the 1825 border treaty with Russia allowed Great Britain to patrol the Stikine and granted it access to the mouth of the river. Hundreds of gold-seekers came north between 1861 and 1865, flooding from the Fraser River strike farther south.

This was exactly the scenario the Imperial government had feared, and it went so far as to try to come up with ways to manage the flood of people, including discussing a permit that would allow prospectors to hunt for gold legally.

That never came to pass, however, as the Stikine strike declined and the American Civil War ended, allowing the Alaska Purchase to take place. The influx of gold seekers would come in the decade after the Purchase as a gold rush to Sitka was followed by one at Juneau and in the Fortymile River country of Interior Alaska.