Apply for the job and let your boss know that you're interested in the position. 

Since he didn't ask you, go ahead and ask him but do it quickly before they find someone else. If you don't like the reason he gives you can apply elsewhere or do something else at that p[oint.

tell him you're going to apply for it, then apply. good luck.

Apply. Sometimes bosses are not in a hurry to lose an employee who does a good job for them. But, it could also mean you are not ready. I am assuming he is not the one making the decision. If he is, and he thinks you are qualified or he wanted you, he would tell you or just promote you. But, the hirer will probably call him and ask about you before you even get an interview. If he does not say good things, you won't get the other job.  It could be he does not want to lose you but won't lie about it to hold you back.

I think you should definitely apply for it. Assuming that he thinks you are not qualified is just a waste of energy on your part. It could actually be because he doesn't want to go through the hiring process of finding someone to fill your position if you are gone. There are other possible explanations as you can see. Why do you only want to look at one negative one?