My nine-year-old daughter suggested that the fact that aliens aren't mentioned in the Bible gave us good reason to think there aren't any aliens. I countered that dolphins aren't mentioned in the Bible either. My daughter noted that kangaroos aren't either, but she thought that aliens were the sort of thing that, if they existed, the Bible would mention them. I thought there was something to that idea, but perhaps only a weaker claim can be made: the fact that the Bible doesn't mention aliens gives us a good reason to think that humans aren't going to meet up with them in this life. For if we are going to meet up with them, we would need the sort of ethical guidance that we expect from Scripture.
I don't think this is a very powerful argument against the claim that there will be human-alien contact. After all, as long as the aliens appear to be rational beings subject to moral constraints we have good reason to think that they are in the image and likeness of God just as much as we are, and we can apply Scriptural principles. But I do think, nonetheless, that the silence of Scripture is some evidence against humans meeting up with aliens in this life.
Note added later: I definitely should have included Tradition alongside Scripture. See the comments.