Career Advice for Engineer

I was a systems engineering major that graduated in May 2014. Not coming from the traditional financial route, I was able to get a graduate internship for 6 months at a fairly large investment bank. It is close to being a BB, but coming as an engineer I was happy to get it being a front office role. The only thing that is weird to me is that this is for 6 months. Does not follow normal recruitment like most banks. I am in about my 3rd month at work. A full time job opened up in another department that I think I would really enjoy and excel in the future. There is no clause in my contract that i have to make the full 6 months, but I was wondering what to do. Do I just apply online and see what happens? Or, do I talk to my manager about it since I know that he knows some of the people doing the hiring? The main thing that concerns me is that I do not want to tip the boat over by leaving early and won't be able to give the other 3 months of work. Also, I have a chance to move into a full time position or even extend the internship again at my current role. Thanks.