The Mukteshvara Temple is found to be the earliest work from the Somavamshi period. Most scholars believe the temple is the successor to Parashurameshvara Temple and built earlier to the Brahmeswara Temple (1060 CE). Percy Brown puts the date of construction of the temple to 950 CE. The presence of a torana, which is not part of any other temple in the region, makes this temple unique and some of the representations indicate the builders were starters of a new culture.

K.C. Panigrahi places the temple to be built during 966 CE and postulates that the Somavamshi king Yayati I built the temple. He also associates the legend of Kirtivassa to this temple, but the postulation is not accepted as Kirtivasa is associated with Lingaraja, though both were built at the same time for the same deity, Shiva. There is no historic evidence to conclude that Yayati had built the temple.