Teaching model preferences of university students and the factors explaining these preferences may give ideas to educators and decision-makers to design future innovative higher education systems. For this reason, this study aims to examine how some factors affect university students' teaching model preferences (face-to-face, online and hybrid) in detail. The factors of the study were gender, opinions about the complexity of the learning management system, sufficiency of digital materials, knowing how to solve problems during online learning, course participation preferences, online teaching methods preferences (synchronous, asynchronous or both), and finally community of inquiry elements (teaching, social and cognitive presence levels). 5504 university students participated in the study and the data were collected by an online questionnaire. Two-way contingency table analyses using Pearson X^2 method and a multinomial logistic regression model (MLR) were applied to determine the factors affecting the teaching model preferences. The results revealed that 71.2% of students preferred to use online supported models (online and hybrid) while only 28.8% of them preferred a wholly face-to-face model. Interestingly, more than half of the females preferred face-to-face and hybrid, while more than half of the males preferred online education. The tendency to prefer online education was related to students' problem solving competencies in the online environment and the learning management system not being complicated for them. This study indicated the relationship of the teaching model preferences with the other factors and community of inquiry elements.