Old post, but here's my .2 for any other people who might be interested:
I recommend saying something like this: "Hi [contact person], this is John Smith. I applied for your [xyz] position last week and would like to meet with you in person to tell you more about my qualifications. Do you have any afternoons free next week?"
What you want is an interview, right? (Well you want a job of course, but the interview is the next logical step.) So ask for that.
I'm not wild about your wording, "progressing with applications..." or with Ellie Kesselman's suggestion, although both are ok. My objection to those choices is that they don't signify strong interest, and even worse, do not directly address what you want. You don't care how their search is progressing, nor do you care what the status of your application is. Don't ask about something you don't really care about. It wastes time (yours and theirs) and is disingenuous.
Your reason for calling this company is to schedule an interview. So cut to the chase and ask for it.
If that feels too indelicate, remember that there are people doing this very thing at this very moment to good effect, and some of them are applying for jobs you want.