The Czech weekly Respekt said on its website that two of the suspected spies were already in Prague working as diplomats while a third was about to arrive.
"We have no comment," Czech foreign ministry spokeswoman Michaela Lagronova told AFP, declining to either confirm or deny the claim.
Alexei Kolmakov, spokesman for the Russian embassy in Prague, similarly refused to respond to the report.
An aide to the Czech ambassador in Moscow speaking to AFP on condition of anonymity said the foreign ministry in Prague had ordered officials to avoid speaking on the matter.
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Wanting to settle the case discreetly and avoid damaging ties with Moscow, Prague simply declined to renew visas for the two diplomats and refused to issue a visa for the third, Respekt reported.
Russian authorities have responded tit-for-tat by refusing to renew the visa of a Czech diplomat accredited to Moscow and preventing the arrival of another, Respekt said.
Tensions have mounted between Russia and former Soviet satellite nations, but relations have been less stressed between Moscow and Prague, where leftist Czech President Milos Zeman has consistently fostered ties with the Kremlin.
About 125 people work at the Russian embassy in Prague, according to Respekt.
Russian secret services have become more active in the Czech Republic in recent years, according to Czech intelligence.