"The laws of the United States hold that a legal entity (like a corporation or non-profit organization) shall be treated under the law as a person except when otherwise noted. This rule of construction is specified in 1 U.S.C. §1 (United States Code), which states:
In determining the meaning of any Act of Congress, unless the context indicates otherwise—
the words "person" and "whoever" include corporations, companies, associations, firms, partnerships, societies, and joint stock companies, as well as individuals;"
If a corporation can own patents and have legal personhood, then you might get to the point where an AI is the corporation, and thereby could own patents. I am thinking of the DAO (Distributed Autonomous Corporation). I am also thinking of the Cat series of novels by Joan D. Vinge, which contain an AI run corporation [3].
Another consideration is that we are seeing AIs invent things now in the fields of medicine, material science, music and perhaps others. If AIs own these inventions then whoever owns the AI owns the inventions.
Given the DAO, if an AI can own assets then I don't see any way an AI cannot own a patent.
Yet another angle though is liability. If an asset owned by the AI is found to be the cause of someone getting injured, then who is at fault? Who has to pay damages?
[1] https://en.wikipedia.org/wiki/Corporate_personhood#Case_law_...