The report is the latest setback to hit the Japanese car maker and comes just days after it stopped deliveries of the vehicle to the US and Canada.
Several safety concerns have forced Toyota to recall more than eight million cars globally, due to safety issues, including faulty accelerators.
The Lexus GX 460 is sold in the Middle East and Russia, as well as US and Canada.
The bulk of Lexus' GX 460s, around 5,400, have been sold in the US. About 6,000 of the models have been sold in total.
The car maker, in response to the report, said it would test its other SUVs. These include the Land Cruiser, Land Cruiser Prado and Rav4.
The last time Consumer Reports urged consumers not to buy a car was in 2001.
Toyota said it was determined to identify and correct the issue.