How to get a PE firm to hire you into a portfolio company?

How can you motivate a PE (or growth equity, or venture) firm to refer you to a portfolio company for a corporate strategy or corporate development position? I'm sure you'd have to interview with portfolio company management, but that the referral would have sway coming from the owner.

For my part, I have a banking background, and would like a corporate strategy / development role soon, but also get reached out to a lot by PE firms, some of which have attractive portfolio companies I could add value to.

I'd also be interested in PE itself as a second-choice, so don't want to upset anyone by starting a discussion under the pretense that I'd want to work for them, and then surprising them by asking how I could instead work for a company they own.

Ideas on how to approach this? Who at the PE firm would you have to influence? Is a recruiter, or a junior person, enough, if that's the only person you know?

Alternatively, if you think this idea misguided or missing something important, please explain how or what.