JLR is keeping staff to coordinate administrative procedures, one source told the newspaper.
JLR told Automotive News Europe that the report was not correct and it continues to serve its Russian customers.
Volvo confirmed it has reduced the number of employees it has in Russia.
"We have adapted our presence in the Russian market and scaled down the size of our workforce in the country," the automaker said in an emailed statement to Automotive News Europe.
Volvo in February suspended sales in Russia, which last year accounted for about 3 percent of its vehicle sales.
The automaker plans to continue warranty support in the country and is ready to pay for parts via parallel imports, Kommersant reported citing a source.
Sales of Jaguar Land Rover vehicles in Russia fell 6 percent to 6,909 last year, according to data from the Moscow-based industry association AEB. Volvo's 12-month vehicle sales increased 13 percent to 9,088.
Staff correspondent Nick Gibbs and Reuters contributed to this report