In the book Lashon Hakodesh, the author includes the word chatul חתול - "cat" in a list of Hebrew words that appear in rabbinic literature but do not appear in the Tanach. This observation leads to two questions: a) Why are there no mentions of cats in the Tanach, and b) where did the word chatul come from?
Regarding cats in the bible, it depends on what kind of cat. Despite the claim of Yehuda Feliks, I don't think that this is identical to the case of the word charuv חרוב - "carob", which doesn't appear in the Tanach, yet certainly was present in the Land of Israel in biblical times. Domesticated house cats were not found in biblical Israel - and they weren't found in Babylon or Greece either at the same time. They were domesticated in Egypt, where they were revered as divine beings (perhaps another reason the Tanach did not discuss them). Only later was the house cat introduced to other parts of Europe and Asia, and the cat does feature in Talmudic literature.
Wild cats, however, were present - they just weren't called chatulim. Two types of wild animals found in Yeshaya 13:21-22 are the tziyim ציים and the iyim איים. Klein writes that according to some scholars tzi צי is related to the Arabic dayuwan, meaning "wild cat". And while most modern commentaries and translations identify the iyim as "jackals", the Aramaic Targum to the verse translates them as חתולין chatulin - in the context, clearly referring to a wild cat as well.
Where does the word chatul originate? A folk etymology connects the word to the root חתל (only found in Yechezkel 16:4) meaning "to wrap up"and is the root of the word diaper - chitul חיתול. They base this on the gemara (Eruvin 100b), which praises the cat for its modesty, because of the way it covers up its waste. However, there doesn't seem to be any linguistic evidence to this theory.
Others see the similarity between the word chatul and the English word "cat" (as well as many other European languages - Spanish gato, French chat, German katz, etc) and say that all those words come from a common source (or even go so far as to say they all came from Hebrew). While there are some examples of words that go back to roots shared by Semitic and Indo-European languages, the evidence is usually very scarce, and so I don't want to take that route without caution.
Normally, I would turn to Klein's dictionary, but all he says is that chatul is related to the Aramaic chatula חתולא. And since the word never appears in the Tanach, my biblical dictionaries and commentaries couldn't help. Luckily, I found this fascinating article by John Huehnergard of Harvard University, entitled Qitta: Arabic cats. In it he discusses a surprisingly large number of words in Arabic for "cat" including a few that have Hebrew cognates.
Most relevant to our discussion is the Arabic word haytal, which he says may have originally meant both "cat" and "dog", He writes that
It seems reasonable to associate the word with the verb hatila 'to prattle, talk nonsense' and its adjective hatil 'garrulous, foolish'.If this is the case, the word is cognate with the name Hattil חטיל (which appears in Ezra 2:57) and to which the Encyclopedia Mikrait associates the meaning "to prattle". There is of course a difference in that Hattil has a "tet" and chatul has a "tav", but despite that, he writes:
One also wonders whether the word is connected with Mishnaic (and later) Hebrew hatul and Jewish Aramaic htula
His most interesting comment though, is the following:
All of these may have been influenced by medieval Latin cat(t)ulus 'kitten,' i.e., small cat(t)us.
So instead of deriving from some ancient common word meaning "cat", the Arabic and Hebrew may have been influenced by one in common use. (The Latin and Greek, as well as another Arabic term for cat - kitta - all may ultimately derive from an Egyptian word). This is a much more plausible, or at least more provable, explanation.
Another word that Huehnergard mentions is the Arabic sinnawr, which is cognate with the Aramaic shunra שונרא. Many of us are familiar with this term from the song Chad Gadya. I had always assumed that chatul was Hebrew and shunra was Aramaic, but now I see that chatula also appears in Aramaic and the two terms seem interchangeable (see both used in the same section of Bava Batra 80b). The article says that the word likely has Akkadian roots, but Steinsaltz suggests that the word might derive from the Greek sainouros, meaning "something that wags its tail" or "a flatterer" (oura means "tail" in Greek, and makes up part of the word "squirrel").
So overall, we see an interesting parallel here. Originally we find only rare words for "cat" in Hebrew, and today it's one of the first words learned by children in Israel. And if millennia ago domesticated cats were not found in this land, today you can't go anywhere without running into them...