After taking the bronze medal at the 2016 CS Finlandia Trophy, Kovtun finished seventh at both of his Grand Prix assignments, the 2016 Skate America and 2016 Cup of China. At the 2017 Russian Championships, he received the bronze medal, having finished third to Mikhail Kolyada and Alexander Samarin. He said that he had begun consulting a psychologist. He won the silver medal at the 2017 European Championships, earning new personal bests in the short program, free skate and overall. He placed eleventh at the 2017 World Championships.