I'm an intern right now and my term is almost up. Here towards the end of my internship I've started doing some work for another team based on my interests. I initially met with the manager on that team last week for coffee and we talked about a range of stuff including my long-term interests before she gave me some work to do. During that meeting she told me about a post-grad position that they're hiring for; I'm done with school in June so I'm definitely interested. I really like them too -- today she invited me to join the team for lunch and it was a good time.
Basically it feels like they might be interested but I'm not sure the best strategy for approaching this. Should I straight up send an email expressing my interest? I've only done a little bit of work for them and like I said my internship is about to be over, so I didn't have THAT much time to get to know them. But I'm almost out of time and think I should make a move.
What steps should I take to show them that I'm interested in joining their team?