Genesis 10 and 1 Chronicles 1 list Asshur among Shem's sons. The same Hebrew name is used in Scripture for Assyria, which later became one of the ancient Near East's dominant empires and conquered the northern kingdom of Israel.
Genesis 10:11 has a grammatical ambiguity over whether Asshur or Nimrod went from the land into Assyria, so detailed claims about the ancestral figure should be cautious.