[2] Kuchayev made his senior debut with CSKA on 2 April 2017, in a 2–1 Russian Premier League win over Krylia Sovetov Samara.

[3] On 6 May 2017, Kuchayev tore his cruciate ligament in his left knee during a 6–0 home win over Arsenal Tula, keeping him out for six months.

[6] On 8 August 2020, Kuchayev scored his first goal in the Russian Premier League on the first day of the season in a 2–0 win over Khimki.

[14] Having represented Russia at various youth levels, Kuchayev scored two goals in nine matches during the 2021 UEFA European U-21 Championship qualifying, helping his team reach for the final tournament.

[17] On 2 November 2020, Kuchayev was named in Stanislav Cherchesov's Russia squad for the friendly match against Moldova and the UEFA Nations League fixtures against Turkey and Serbia.