The context of this question is puzzling.
Suppose the qualifications for someone to be interviewed are that the person must have a doctorate in mathematics and experience in discrete mathematics. Under what circumstances would it make sense to invite for an interview people who have not yet graduated from college.
Suppose the qualifications for someone to interviewed are that the person must be older than 17. Under what circumstances would it make sense to require people to be older than 39 in order to be invited to an interview?
The point I am trying to make is that it is hard to write what you are trying to say because it seems to make no sense. Please explain why you would invite people to an interview in order for the interviewer to dismiss them as being unqualified even to be interviewed. Please explain why you would not invite to be interviewed people who qualify for an interview. In short, the idea that there is one set of qualifications for an invitation to be interviewed and a different set of qualifications to be interviewed needs to be explained before good wording can be found.
Of course if the qualifications for an interview and the qualifications for an invitation to be interviewed are the same, your writing problem goes away
not qualified for an interview