The Eastern edge of Russia, close enough to the Bering strait, has been throughout that time frame sparsely populated by people who were neither sea-farers nor probably interested in leaving their land for such an unknown.

Furthermore, any exploration and subsequent settling attempt could have resulted in a very short-lived and localized settling of Alaska that we might not even have a solid evidence of- like the viking settling of Vinland, but without any reliable trace happening to survive.

Given the sheer size of Siberia, amplified tenfold by the technological level and information reach of olden days, any knowledge or hunch the locals may have had of a land beyond the strait probably wouldn't have travelled much farther than their territory.

It took the imperial Russian settling of the area, and the first Kamtchatkan Expedition in 1724 for modern Europeans to 'truly' discover America from the East.