We actually have a concept of extraterrestrial life discussed in the Torah: that of the ???. Obviously however we’re all reddening to an intelligent life that is not privy to divine instructions and lives in its own planet with its own people such as ourselves. So here’s what I can tell you:
There are various Pesukim in Tanach that are “used and abuses” when it comes to this topic. One such Pasuk would be ?????? ????? ?? ?????? etc. If you take Olamim to mean physical worlds, the Pasuk should mean that Hashem’s kingdom is a kingdom “for all worlds”. Now if we’re talking about barren planets with nothing on them, what does that mean? One solution can be to translate the Pasuk as “Your kingdom is a kingdom for all time”, ???? mening time as in ????? ???.
In many places Chazal describe the immensity of our universe, all the millions of stars that are in it etc. and they go on to explain how all this was created for man. Which causes one to say “Wow. Really? Perhaps there’s other life out there?” We do have two Midrashim that are open to this interpretation. The Pasuk in Koheles says ?? ??? ???? ??? ????? – Everything was made properly in its proper time. The Medrash has 3 explanations for this Pasuk. The second is R’ Avahu: We see from here that Hashem has made many universes and destroyed them, ?? ???? ?? ???. This Medrash is sometimes quotes regarding the Ice Ages. The importance of this Medrash is that it opens up the possibility of there having been other worlds similar to ours, albeit in a different time. (The fact that Hashem destroyed them is not a sugn that he made a mistake, rather if there was intelligent life there, they would have brought destruction unto themselves, just like what happened during the times of Noach where they had their own Bechira and messed up.)
There is a Gemara that asks “What does Hashem do at night?” The Gemara provides to answers. The first: exactly what he does during the day! The second answer (there are many Seforim that explain these type of Gemaras) is that Hashem gets into his chariot and rides around eighteen thousand Olamos. (Someone recently told me that this Gemara lists a number if stars, which was about two digits more or less from the number that NASA gives!)
There is a Rishon R. Chasdai Kreshkish who deals with this issue. He brings arguments in favor of, and opposed to extraterrestrial life. Among the ones in favor of: Whether you beleive the world came into being because of Hashem’s desire, or wether it came simply because it had to be so, why couldn’t this desire or neccesity mandate that there be multiple worlds! Moreover, according to our view, which is that Hashem made this world out of his own Ratzon, is Hashem stingy all of a sudden? Why would he stop here? The more He cretes, the more good He’s able to provide (which is the reason why He created us). On the other hand he says: We only find multiplicity of entities regarding things which exist and are mortal. There are many trees, because trees get destroyed. Which is the reason why you need to have more than one tree. Which is why for entities that do not get destroyed, there is no multiplicity. Therefore, says R. Chasdai, since our world cannot be destroyed, there are no other worlds (I also have a hard time understanding that). Another argument is: The One who created all that exists is One, is the simplest and purest sense that One can mean, so that which he brings into existence should also be one. Either because everybody must agree that that which is purely one, will also create things which are purely one. Or you can say that the perfection of that which is created should reflect its creator, therefore you only need one. Now, you can drive a truck through the holes in these arguments, but this is what this Rishon says. He goes on to debunk almost all of his arguments, for and against extraterrestrial life. He concludes by saying that “I cannot get a definitive answer from any of my arguments, but one thing we do see: that the possibility of extraterrestrial life exists.”
In conclusion, we see that although there is no proof in the Torah of extraterrestrial life, we see that such a possibility does exists, and there wouldn’t be a Hashkafic reason to beleive it doesn’t exist, rather it is up to you to look at different interpatations of Pesukim, and contemporary science to formulate an opinion. If I have patience (and if I see people are interested:) I’ll post more!