Kovtun's father Pavel is a figure skating coach but never coached his son. Kovtun's two older brothers were competitive skaters as well and perform in ice shows. Kovtun withdrew from the 2018 National Championships citing injury and wanted to retire from competitive skating, but came back in spring 2018 and returned to former coach Elena Buianova (nee Vodorezova), the 1983 World bronze and a three-time European medalist.