Independently co-invest along side PE?

I've built a relationship with the founder of a small saas company who has grown his business to $8m in ebitda and is looking to exit. 

Is it at all attractive to your typical PE firm if, through my M&A advisors, we pitched this deal to PE with me personally co-investing 15-20% of the equity capital along side the PE's portion, with the balance in debt. And an operational plan for me to run the company post acquisition. 

For context, I was a founder in an adjacent, yet relevant industry for 20 years, my company was acquired by a F500 and I served in a director role for 10 years after the acquisition.

This is an off market deal, that I need the right capital partner to execute. So I'm wondering if this scenario is potentially an attractive one for PE to lead, with myself having a minority equity share but a larger role in the deal process and ongoing operations of the company.

Or more broadly if PE is the right path in this scenario?