Hi, I answered a question on one such route, North Eastern route here:

The quest for the North-West passage is widely storied, but was there the effort placed toward a North-East passage? Or even a direct Northerly one? where I go into some details of an English 1553 expedition that tried to go North around what is today Russia, and I also mention, but don't go into much details into the more famous three attempts by Willem Barentsz in the 1590s that tried the same, none of which succeeded (Barentsz himself died in the final attempt) after which the idea was more or less scrapped.

Following this there were attempts to find a North Western Passage (around Americas) but I can't give much details of those.