Toyota may soon have a fix ready for the troubled Lexus GX460 SUV.

Just days after putting a temporary halt to sales of its Lexus GX460 due to safety concerns, Toyota is reportedly readying a technical fix to overcome a potential rollover problem with the sport-utility vehicle, say reports from Japan.

The latest in a seemingly endless series of safety problems involving the various divisions of the Japanese maker turned up earlier this week when Consumer Reports magazine announced that it was issuing a “Don’t Buy” warning for the new, 2010 GX460.  The non-profit magazine had discovered, during testing, that the SUV might be prone to rolling over under certain conditions.

Toyota, which is facing a record government fine for failing to disclose other safety problems in a timely manner, responded by halting sales and reaching out to the 5,400 owners who’d already purchased a GX since its introduction.

Now, reports Japan’s Nikkei Daily, Toyota is reportedly working up a fix that will, first and foremost, address the vehicle’s electronic stability control system, along with work on “other (unspecified) aspects of the vehicle.”

Consumer Reports pointed its publishing finger at the stability control system, noting that it failed to respond quickly enough during overly-aggressive cornering maneuvers that could cause the rear of the heavy ute to slide.  If the vehicle then hit a curb or some other obstacle, the magazine’s testers felt the 2010 GX460 might be prone to rolling over – though there have been no reported claims of such crashes.

The flap over the GX only exascerbates Toyota’s ongoing problems, which include the record $16.4 million fine the National Highway Traffic Safety Administration has levied against the automaker for reportedly delaying action on a problem involving sticky accelerators. Newly released internal documents show the automaker’s U.S. and Japanese staff debating whether to notify the government of the problem for months before the January 21 recall of 2.3 million Toyota vehicles.

The government has gotten hold of the GX460 that alerted Consumer Reports to the potential rollover problem.

Meanwhile, AutoWeek is reporting that Toyota has decided to conduct its own tests on every SUV model it produces to make sure there aren’ other problem yet to be discovered.

While so-called sudden acceleration is the issue generating most of the headlines involving the Japanese maker, Toyota has also been defending itself, lately, from a raft of lawsuits in which owners claim some of its sport-ute and crossover vehicles are, indeed, prone to rolling over.