I had an interview at a university for a tenure track position. They decided not to give me an offer, but I met a professor there (for the first time) that supported me as a candidate. This professor saw my application, went to my talk, and was not on the search committee, but participated in my campus visit.
I corresponded with this person through e-mail, and the phone, about my career (not just about the position).
Since I didn't get an offer for a job I wanted this year, can I ask this person if they would write me a reference letter for my job search next year?