Advice needed to transition referral to offer

Hey guys, So awhile back I met (through a close mentor) a successful business consultant (founder and director) who had previously offered to help me become connected (and land a desired internship). After our initial meeting (think a 7-9 person group forum) he told me to get in contact with him and he could help me out. I took him up on his request and we met in his office. After getting to know me he asked how he could help and by the end of the conversation I had referrals to 3 firms in the area (to personal friends/colleagues of his). I have since reached out to those referrals to establish contact and meet with 2 of them on Friday. I am ecstatic to become more well-networked, but how should I approach the idea of interning at these firms? Should I be straightforward in my intensions about securing an internship off-cycle for Fall (while I'm in school)? Or should I meet a few times and then broach the subject? He was extremely optimistic that I would be able to land one with one of the firms and was CC'd in all of the emails.

What would you guys do? I am really looking at tactful and mature methods to ensure lasting relationships.

Thanks guys I really appreciate any replies/advice.