Recruiting/Networking Etiquette - Special Case

For the summer, I'm interning at a boutique investment bank that focuses primarily on sell-side advisory. We work with consumer-brands, particularly in apparel, etc.

I'll keep this short - I'm also planning on interviewing full-time for consulting. The particular consulting firm I'm looking at offers an earlier round of interviews (late August to early September) to beat the OCR rush, which I'm planning to do.

However, I'm also interested in exploring some PE firms. I know my chances are slim, especially coming from an undergrad level, but I'm interested in the retail/consumer goods space and I have a good idea of some PE firms that I'd be interested in exploring further.

I'd like to reach out to some alumni who might work at these funds, but I'm currently working on a deal which involves some of these PE firms (ie constant communication). As I'm trying to plan out OCR for late summer/early fall, I'm wondering - what would be the best thing to do if I want to speak with these firms in the context of recruiting?

Should I wait until after my internship is over to introduce myself (which I feel like is a late, late start)? How would I broach the subject that I'm currently interning at a bank that's trying to sell a company to them?

I'm completely new to this, so I'd appreciate any feedback possible. I'm also considering going back to the bank I'm working at for full-time (I'm fairly certain that I'd get a return offer).

Thanks!