He was part of the Soviet Union national team that won the gold medal at the 1956 Summer Olympics.

Salnikov scored two goals and made another in the final match of the 1949 season against Dynamo Moscow, when Spartak narrowly missed out on the Soviet Top League title in a 5–4 defeat that some consider the greatest match of the era.

Salnikov, fearful for his health, made representations to have him transferred to an ordinary prison, and was allegedly told that it would help his case if he moved from Spartak to Dynamo Moscow.

[4] He joined Dynamo Moscow in 1950 and, although unhappy,[4] was part of the first choice lineup between 1950 and 1954, making 113 appearances and scoring 29 goals.

Spartak star Nikita Simonyan considered Salnikov as one of the "golden generation" of Soviet players in the 1950s and 1960s.