Through playing a limited number of games, Kostin was taken with the last pick in the first round of the 2017 NHL Entry Draft by the St. Louis Blues. Initially thought to continue developing in Russia, Kostin was made a free agent after Dynamo Moscow were forced to release all of their players through a violation of KHL rules on 4 July 2017. The following day, Kostin agreed to a three-year entry-level contract with the St. Louis Blues. Kostin has said that he would prefer to play in the NHL for the 2017–18 season, though would not oppose going to the American Hockey League (AHL), the top minor league affiliate for the NHL; however he had no interest in playing in the WHL, or any junior league.