Without more information about your interview and what was said and asked, I would suggest that you recap the high points of the interview, your strengths and how you would support the professor as his student, how the professor would help you grow and learn through his mentorship, and how you would use the experience going forward in your career and life.
A statement of purpose typically includes a brief background followed by a more extensive, in depth explanation of how your background informs your goals for the future with regard to the area of interest.
As an example, many future Physicians Assistant and Pharmacy students state that they want to attend PA or Pharmacy school (or nursing or law or medical school) in order to help others through their work. However, most students miss the mark in not being specific enough.
However, without knowing your academic area, it would be hard to give specific advice.
If he is truly interested to take you on as his student, would you be comfortable asking him to clarify his request?