Metropolitan Kirill said Alexy II, who led services at the cathedral for many years, had expressed a wish to be buried there.
The patriarch's body will be brought to the Cathedral of Christ the Savior later on Saturday, where it will lie in state through the night.
The Patriarch of Moscow and all Russia, who led the Russian Church for 18 years, died at the age of 79 in his residency near the capital on Friday morning.
A senior church official said heart failure was believed to be the cause of death. The patriarch was known to have suffered from health problems in recent years.
Alexy II became patriarch of the Russian Orthodox Church in 1990, shortly before the collapse of the atheist Soviet Union, and presided over a religious revival in Russia, with thousands of churches and monasteries being restored and hundreds of new ones built across the country.