[3] Magomed himself is the grandnephew[4] of the late Ingush World War II ace who served in the Red Army, Murad Ozdoev.

[5][6] He made his Russian Premier League debut on 10 July 2010 for Lokomotiv Moscow in a game against FC Anzhi Makhachkala.

On 14 July 2014, Ozdoyev was loaned by Lokomotiv Moscow to Russian Football Premier League rivals Rubin Kazan for 1 year with buying option.

He scored his first national team goal on 15 November 2016 in a friendly against Romania which finished as a 1–0 victory for Russia in the city of Grozny, where he was born.

[13] On 2 June 2021, he was included in the final squad, making history as the first Caucasian Muslim footballer to represent the Russian side in a major competition.