Rashba (1235-1310) writes that the 13 attributes are considered a davar shebikedusha. Therefore, if there is no minyan, one may recite the 13 attributes as one who is reading verses in the Torah, but not as a prayer.
- Shulchan Aruch codifies Rashba's ruling (O.Ch. 565:4)
- Rama (1520-1572) writes that an individual shouldn't recite Selichos at all.
- Mishna Berurah writes that the Acharonim question Rama's ruling and contend that one may recite Selichos even if there is no minyan.
R. Moshe Feinstein (1895-1986) discusses whether recitation of the thirteen attributes is for the purpose of קידוש שם שמים or whether it is a tefillah. The practical difference is regarding someone who is learning in shul and hears the congregation recite the thirteen attributes. If it's the former, one should recite it with them. If it's the latter, there is no need to recite it with them. While R. Moshe prefers the latter approach, he notes that one should recite it with them unless one is learning in a public setting. (Igros Moshe O.Ch. 3:89)