Born in Mezdra, Genkov began his career in the local Lokomotiv, previously having been a track and field athlete.

On 28 January 2011, Genkov joined Polish Ekstraklasa side Wisła Kraków on a three-and-a-half-year deal for an undisclosed fee from Dynamo Moscow.

Genkov also netted the winning goal in a 2–1 victory over FC Twente, in the last UEFA Europa League group stage match, which lead his team to qualify for the round of 32.

[10] He was not registered for the 1st round of the UEFA Europa League games against Kazakh club Irtysh Pavlodar, which his team lost by an aggregate score of 0–2.

Genkov made his official debut for Levski Sofia on 21 July 2013, in the 1–2 away loss against Botev Plovdiv in an A PFG match.

[13] Receiving his first call-up for an official match in March 2005,[14] he was capped nine times for Bulgaria national under-21 football team, scoring three goals.

Genkov received his first senior international cap for Bulgaria on 17 August 2005 in a friendly match against Turkey, which they won 3–1, coming on as a substitute for Dimitar Berbatov after one hour of play.