Zenit St Petersburg's largest supporters' group has called on the club not to buy black or gay players and urged it to maintain its "national identity".
The Landscrona group posted the demands on its website in what it described as a "manifesto".
Zenit are the only leading Russian club never to have signed an African player, and are based in a city known for strongly nationalist and rightwing attitudes.
"We're not racists but we see the absence of black players at Zenit as an important tradition," the Landscrona "Selection 12 manifesto" read.
"It would allow Zenit to maintain the national identity of the club, which is the symbol of St Petersburg."
The organisation said it wanted to see only "players from other brotherly Slav nations, such as Ukraine and Belarus, as well as from the Baltic states and Scandinavia".
It said this was because St Petersburg shared "the same mentality and historical and cultural background as these nations".
Landscrona also said it did not want to see "sexual minorities" in the team.
Media reports in St Petersburg have claimed that several well-known black players have turned down lucrative offers from the lavishly-backed club because of threats from fans.
Zenit refused to comment on the fans' group's "manifesto", but ex-Zenit and Russia striker Alexander Panov said: "All clubs around the world have black players.
"If they are absent from Zenit, it's Zenit's problem. I don't think fans should demand the club buy or don't buy certain players."