Let me preface this by saying that I am not an expert in Arabic or Asian folk traditions, but I have looked into this, honestly hoping to find a connection. There appears to be none.

A common mistake for people to make is to look at generic qualities of various international folkloric motifs and/or things that have similar sounding names, and consequently to conclude that they must be related. Drilling down, we often find that the similarities are not as profound as initially thought and there is no good reason to conclude that there was a historical connection between far-flung motifs.

In this case, the 狐狸精, húlijīng, literally “fox spirit” in Chinese folklore, includes the term jīng, which sounds vaguely like the Arabic جن, jinn (sometimes appearing in transliteration as djinn), which is the source of the English word “genie.” I cannot find evidence that the two terms (the Arabic term draws on a Semitic root referencing its invisibility and amorphous forms) are linguistically related, despite sounding vaguely (but only vaguely) alike. Perhaps there is a linguist here who can demonstrate that I am wrong on that count. In fact, let that be my first wish.

Then there is the question as to whether the two traditional supernatural beings are similar enough to warrant speculation about a historical connection – beyond the question of linguistics. We must remember that the idea of supernatural beings is international. While historical connections can be demonstrated for some of these, vague similarities do not necessarily justify concluding that such connections exist. The common denominator of the human experience causes some traditions to seem similar in vague ways, even when there is no connection.

The Arabic jinn is more familiar to the English-speaking world thanks to many (some very early) translations of the Arabian Nights. The resulting English-language genie has consequently become part of modern pop culture in the English-speaking world – and beyond as various films have been translated and presented internationally. These entities were typically invisible (although they can assume various forms) and they are extremely dangerous. It appears that jinn have pre-Islamic roots, but whether they are demoted early deities, or lesser spirits in the earliest incarnations is unclear.

The Chinese term jīng can be translated as “essence, energy, or spirit.” The term can be used in several very different contexts, but when it is used to indicate a húlijīng, it is more specifically a supernatural being, hence the origin of this question. That said, the “fox spirit” is different from the Arabic jinn. The Chinese fox spirit and the many other entities that the Chinese term describes are far less singular than the Arabic jinn (the Arabic entities are also diverse, but they belong to the same family in a way that is not necessarily the case when it comes to those included with the Chinese term). All folklore is by its nature diverse and can often be contradictory (although it is often described popularly in absolute, singular terms). It appears, however, that the possibilities of the Arabic jinn are less broad than the Chinese húlijīng, which includes a wide range of possible manifestations (responding to the enormity of Chinese history and its expansive geography with its corresponding diverse cultures).

Again, let me stress that I am not an expert in either culture. I am merely looking at what evidence I can find, and I can only cast doubt on the idea of a connection, based on what I know about how folklore functions and is often misunderstood. I hope helps at least a little.

edit: I see in a comment that may have been removed, that there is reason to question whether this answer violates the rules /r/AskHistorians – a fair question it seems to me. Many sustained answers on this subreddit come from people who can address a question, but whose knowledge and responses can be augmented by others. It is a rare question that is a perfect fit for any one of the many excellent volunteers who fill this sub with such wonderful responses. The universe of possibilities in the history of the world is vast.

Too often, the questions presented by the past present us with something that is close to our training, but which requires some delving in. What I saw that I could offer to this question was [training in folkloristics] (https://www.academia.edu/38773351/Nazis_Trolls_and_the_Grateful_Dead) and some training in linguistics, providing me with the academic tools to address this question with a method needed to evaluate information readily available. Recognizing and acknowledging that I am not an authority in this specific geographic area, I established the parameters that are needed to evaluate the information. Mine is not a perfect answer, but it provides the structure to understand the issues, and fulfilling at least part of my wish, others have stepped forward with additional linguistic insight into the Asian term.

I can confirm what u/itsallfolklore has said, coming from historical linguistics. It's entirely coincidence.

精 is a well-attested case of semantic shift, i.e. the meaning of a word changing over time. This happens regularly in all languages and it's the reason "black", "blue", "bleach", "blank" all come from a common source, and why awful and awesome have opposite meanings even though both mean "with awe".

In the case of 精, the composition of the character tells us that it's pronounced something like 青 (the phonetic component) but semantically related to 米 (grain, rice). Not all Chinese characters have this sort of composition of semantics+phonetics, but this one does.

Much like "clean" in English is derived from the meaning "small" (preserved in German klein), the path that 精 took was from an initial meaning of "polished/refined rice" into a sense of "pure" into "essence" into "spirit". This is as u/The9isback says.

جِنّ meanwhile is derived from a root meaning "to cover/conceal". This isn't too far from the "veil" that people in paranormal circles talk about. The Jinn are concealed form us until the end times in Islamic tradition. The 2 n's here are significant in the Romanised spelling, as the Arabic root is ج ن ن‎. That tiny little w-looking thing above the ن in جِنّ is a ḍamma, an indicator that the letter below it is actually there twice. This root, j n n, is one which reconstructs to proto-Semitic, and is found in Hebrew as well (but again having undergone semantic shift), reconstructed for proto-Semitic as *gnn/gny/gnˀ meaning "to enclose, to protect, to shelter" with other cognates in Syriac, Accadian, Sabaean and Mehri.

When looking at these kinds of possible connections, it's important to look at cognates across the two language families, see what sort of semantic drift has happened (it always happens), and what sort of sound changes have happened from the ancestral language. The velar nasal coda (the ng sound) in jīng is a problem, but not a huge one. Nasals can change. Still, in this case though, it's not one that's typical in Arabic, nor is it one that's undergone much loss in Sinitic. So already that would be a red flag. In this case at least 精 hasn't changed that much in pronunciation, but it's still a pretty bad match for j n n in Arabic. This is made worse by the system of trilateral roots (j n n as the base) in Arabic, almost guaranteeing the vowels are a coincidence. You start out with a three-letter root, like j n n or s j d, and then the different parts of speech, agent/patient encoding, tense, number, etc, are all managed by fairly regular vowel patterns and prefixes. Because of this, vowels are rarely useful in these kinds of comparisons.

Mandarin is also rarely a good representation of how Chinese used to be pronounced, as a general rule, although Cantonese, Hakka etc are only marginally better. We have *g as the onset in Semitic, still pronounced /g/ in Egyptian Arabic but otherwise /d͡ʒ/ in most dialects of Arabic and also English Jinn. Sinitic was *ts but now /tɕ/ in Mandarin. Today, these are basically the same for speakers of English, but they would not have been whatsoever at the earliest points of Arabic-Chinese contact, so we can rule out a common origin of some hypothesised proto-Sino-Semitic. And we have heaps of attestation for 精 well before that time anyway so we can rule out borrowing.

So, yeah, complete and total coincidence, and even then you really need to stretch the modern definitions of both 精 and جِنّ quite a bit to get a reasonable overlap.

edited for better phrasing.