Converting networking with senior to interview/internship process?

I'm currently a rising sophomore looking for 2025 internships. Today I had a networking call with a partner at a PE firm (school alum) that takes interns. However, I don't think there is a concrete application process for internships. The call went really well, but since he was a partner I didn't want to mention internships and specifically ask him then because I was more focused on building a relationship with him and thought it might be awkward for him since he's high up (might have messed up lol). I'd be really interested in interning here - how should I proceed? In the thank you email, should I mention potential internships? Not really sure what to do since there doesn't seem to be an application process where I can ask him for a referral and I really don't know anything about the process/timeline at the firm. For background, I have a pretty good freshman internship at a co-investment firm and go to a semi-target.