The Russian government has yet to comment on the report.
Brutal dictator Assad fled to Russia, his backers in the civil war, after being toppled by jihadi rebels.
Assad, 60, has not been seen in public since moving to Russia.
New authorities in Syria have called for his extradition, which the Kremlin has refused.
The deposed president, his wife, and hundreds of relatives, along with political, military, and business cronies, are included in a list of 417 individuals and companies under UK sanctions.
The High Court was told in 2020 that Assad is believed to have a frozen account with HSBC in London with a balance of more than $51.5 million (£40 million).