At the 2014 Russian Championships, Kovtun placed second in the short program and first in the free skate. He was awarded the gold medal ahead of three-time Olympic medalist Evgeni Plushenko. After Kovtun again placed fifth at the European Championships, Russia's sole spot in the men's event at the 2014 Winter Olympics in Sochi was assigned to Plushenko. Kovtun was sent to the 2014 World Championships in Saitama, Japan. He placed seventh in the short program, fifth in the free skate, and finished fourth overall behind Spain's Javier Fernández.