I've been giving this a lot of thought and when you really think about it, it makes a lot of sense. After doing some research, I am now convinced beyond all doubt that Jiren is a being of this nature.
In the Buddhist belief system, when a being reaches the highest level of spiritual awakening, they enter a state known as enlightenment.
Why is this relevant to Jiren?
Jiren is not a God. That much is clear
However, it is beyond doubt that he has characteristics resembling a God. Indeed, Whis commented that his power resembled that of a God of Destruction. Perhaps even surpassing one.
Jiren has shown incredible power, none more so than the power from his eyes.
This is only possible through Enlightenment.
There is one particular belief that stands out with regards to Jiren.
The Third Eye
In the Buddhist belief system, awakening the Third Eye provides the user with a state of near Clairvoyance and heightened perception. People who have unlocked this potential can create mind worlds via meditation. They achieve a higher state of being, a higher consciousness. It could be argued in fact, that this is power beyond the Gods. Who does that sound like? It's no accident that there is such focus on Jiren's eyes.
Jiren is no God. He has transcended them. He is at one with the Universe.
When Goku awakened the power of Ultra Instinct, he merely has awoken one piece of the puzzle. Notice how calm, relaxed and almost meditative he was during his fight with Jiren? It's no coincidence, he unlocked an early stage of this power.
Remember what Dragonball stems from?
Journey to the West
At the end of that story, the main protagonist Sun Wukong achieves (you guessed it) Buddhahood.