The Qataris, both from the Qatar Greco-Roman wrestling team, were arrested in transit at Moscow's Sheremetyevo airport on 26 February on suspicion of carrying undeclared foreign currency with them. No charges have been filed.
This followed Doha's arrest of two Russian intelligence agents, who are charged with assassinating a leading Chechen fighter, the former president of the breakaway republic Zelimkhan Yandarbiyev, in the Qatari capital on 13 February.
The FSB security service, which according to Russian press reports has taken custody of the two Qataris, declined to comment on their whereabouts.
The Qatari embassy in Moscow also maintained a diplomatic silence amid reports that negotiations are taking place between the two countries.
"We have been ordered not to comment on this case," said an embassy official.
Moscow's respected Kommersant daily identified the two detained Qataris as Nasir Ibrahim Saad al-Madhihiki, an official with the Qatar Greco-Roman wrestling team and Ibad Akhmedov, an Azerbaijani who has Qatari citizenship and competes for the team.
Qatari officials have confirmed the identifications.
The Qataris were detained when customs discovered that al-Makhihiki was carrying $7200 that he did not declare, according to Alexander Dubrovksy, their Belarussian team trainer who was stopped along with the two men and later released.
Russia's new Foreign Minister Sergei Lavrov on Wednesday reiterated Moscow's demands that Qatar free the two Russian agents.
Moscow has denied its agents had anything to do with the murder of Yandarbiyev, who died after his car blew up in Doha as he was returning home from Friday prayers.