Higher education in the twenty-first century is a key factor in increasing the country’s efficiency and competitiveness, as it provides the modern labor market with a competent workforce. The state should create a variety of conditions that stimulate the effective operation of universities, especially if these are innovative organizations of an entrepreneurial type, capable of quickly adapting to external changes based on the introduction of educational and organizational innovations. The study is devoted to developing a set of models for analyzing trends in changes in external environmental factors and their impact on the activities of Ukrainian innovation-active universities (IAUs). It is proposed to consider the external and internal attractiveness of the higher education system (HES) as factors of the external environment of IAUs. Based on the application of rating, cluster, and indicator analyses, a portrait of the attractiveness of HES is built, and its strengths and weaknesses are highlighted. A set of models for predicting indicators of external and internal attractiveness of IAUs is developed. The Granger causality test showed strong relationships between indicators of the external and internal environment with lag 1 and 3 years. Impulse and variance analyses in VAR models confirmed 70% of influence of external environments in internal. Using ARIMA models, forecasting the overall attractiveness of HES was carried out that showed stable tendency to asymptote.