How to express interest in writing...

Hi...
I am a new grad. I had a baby 5 months ago, and while I was being sewn up from my c-section (ugh) my husband was chatting with the nurse about me. She told him that the hospital will have at least one residency in L&D this spring. I really want that job! I want to send the nurse manager my resume and a cover letter but I'm not sure how to word the cover letter since there is no job to apply for yet. Any thoughts?

Thanks!
Carrie