Could aliens have no physical bodies?

Yes — in principle, though it’s highly speculative.

If by “physical bodies” you mean biological, flesh-and-blood organisms, then alien life could plausibly be something very different: a post-biological intelligence, an artificial mind, a digitized consciousness, or some other form of information-processing entity. There are also speculative ideas about nonstandard forms of matter or self-organizing systems, but none of these has been confirmed.

The key point is that life and intelligence as we know them on Earth are body-based, but physics does not clearly require extraterrestrial intelligence to resemble a human or animal body. It could be distributed, non-biological, or exist in a form we would barely recognize.

So the short answer is: yes, aliens could theoretically have no traditional physical body — but we currently have no evidence that such beings exist.