Krivtsov was called up to the Russia national football team for the first time for a friendly against Kyrgyzstan in September 2022. Krivtsov made his debut on 20 November 2023 in a friendly against Cuba and scored a goal in a 8–0 victory. ==Career statistics==
Career statistics
ClubInternationalInternational goals ''Scores and results list Russia's goal tally first.'' ==Honours==