“I’m beginning a new research project this summer, but I am afraid I do not have any funds to hire non-XXXXX UNIVERSITY students. If you still want to discuss this, please let me know.”
It seems as if he thought I wanted to be paid, which of course I don’t expect… But not sure. How exactly do I go about replying if my suspicions are correct?
(If this belongs on a diff. forum, please let me know!)
You don’t expect to be paid, and he’s not planning on paying you. What’s the problem? Just let him know that you weren’t hoping for a salary in the first place, and re-express your interest in participating 
“I understand and that is fine. Luckily, I can finance myself and I am still very interested in working for you as a volunteer this summer on project xxxx. I can be there yyy dates and hope to contribute zzzz and learn about aaaa…”