I have contacted a potential PhD supervisor and he sent me back that I appear to be a motivated and interested student but his funding does not allow him to supplement a student at PhD level. However, I have my own funds, and I intend to fund myself through my PhD studies for 1 year. How do I raise this issue formally with him?
If a professor says "my funding does not allow me to supplement a student at the PhD level," he is explicitly saying that he cannot take on another student due to lack of funding. It's implied as a prospective PhD student that you are simultaneously looking for funding when applying to schools and/or contacting potential advisors.
That being said, you have mentioned that your situation is different than the norm. By all means, reply back thanking him for his consideration and bring up the fact that you have your own funding and exactly how long you plan to self-fund yourself. Perhaps he will be able to take you on, perhaps not.
Personal side note: Before responding to him, make sure you are certain about self-funding, even for a year. It costs quite a bit just to attend a PhD program, let alone to live during that year. There's a reason that the expectation of PhD programs (or advisors) is to offer funding to their accepted students. As a student, handling graduate-level studies and research can be stressful; handling money issues on top of that can sometimes be too much.