More can be written, but you might like to read these discussions from the FAQ section "American Expansion":
"Did the British Empire ever have interest in Alaska?" by /u/The_Alaskan
"Why did Alaska go to the United States and not Canada?" by /u/The_Alaskan
"Did the UK consider trying to conquer Russian Alaska during the 19th century (during the Crimean War, for example)?" by /u/The_Alaskan
This is not to discourage discussion. More questions, data, and debate are welcome.