Greco-Roman classical writers 

Greco-Roman classical writers such as Julius Africanus, Marcus Velleius Paterculus, and Diodorus Siculus dated the founding of Assyria to various dates between 2284 BC and 2057 BC, listing the earliest king as Belus or Ninus.

According to the Biblical generations 

According to the Biblical generations of Noah, which appears to have been largely compiled between the 7th and 5th centuries BC, the city of Aššur was allegedly founded by a biblical Ashur the son of Shem, who was deified by later generations as the city's patron god. Assyrian tradition itself lists the first king of Assyria as the 25th century BC Tudiya, and an early urbanized Assyrian king named Ushpia (c. 2050 BC) as having dedicated the first temple to the god Ashur in the city in the mid-21st century BC. It is highly likely that the city was named in honor of its patron Assyrian god with the same name.