Asparuhov was also nominated for the 1965 Ballon d'Or award, finishing eighth in the final standings.

[5] Asparuhov began his senior career at Levski Sofia in the end of 1959–60 season at the age of 17.

He made his debut on 5 June 1960 in a 1–0 home loss against Lokomotiv Sofia, coming on as a second-half substitute.

A week later, in the second leg of Botev's European tie against Steaua, Asparuhov scored his first-ever hat-trick in a resounding 5–1 home victory.

He also scored in a 4–0 away win over Shamrock Rovers on 24 October 1962 and became a top scorer of the tournament with 6 goals.

He made his World Cup debut in the second group game against Hungary at Estadio Braden Copper Co. in Rancagua on 3 June 1962.

During the World Cup he scored Bulgaria's only goal in a 1–3 loss against Hungary at Old Trafford in Manchester.