Toyota appears to be reaching a settlement with the National Highway Traffic Safety Administration regarding the unintended acceleration issues that have plagued the maker.

Toyota may soon write a check for more than $1 billion to settle a government investigation related to its sudden acceleration problems, avoiding the possibility of criminal prosecution.

Several media outlets, including the Wall Street Journal and the Detroit News, are citing “unnamed sources familiar with the negotiations” to describe what appears to be a deal that would end a four-year investigation by the U.S. Department of Justice. The government had been looking into the possibility that Toyota had intentionally misled federal regulators about possible defects involving its vehicles.

Starting in late 2009, Toyota ordered a series of recalls covering more than 14 million vehicles worldwide for various problems that could potentially cause them to surge out of control. Up to that point, more than 3,000 complaints had been received by both the maker and federal regulators, the National Highway Traffic Safety Administration (NHTSA) linking the problems to at least five deaths.

Among the internal company documents released during government hearings in early 2010, one celebrated the fact that Toyota saved millions of dollars by convincing the NHTSA to drop plans for an earlier recall.

But the issue ultimately became a costly one for the world’s largest automaker.

The federal safety agency eventually fined Toyota about $70 million for failing to respond to potential safety issues in a timely manner, as required by law.

Meanwhile, Toyota has paid $29 million to settle charges by 29 state attorneys general that it knew about, but failed to act on, safety-related problems. That settlement also prevents Toyota from advertising the safety of its vehicles without having engineering data to back up its claims.

The maker reached a $1 billion civil settlement, the largest ever for the auto industry, to cover claims related to the sudden acceleration issue in December 2012. And it has settled a number of other individual legal claims since then – though it has also fought a number of lawsuits involving owners who claimed to have been injured in crashes related to sudden acceleration problems, winning a number of them.

Several investigations initiated by NHTSA, including one conducted by NASA, found no clear evidence of the mysterious electronic gremlins some owners alleged could cause Toyota vehicles to surge out of control.

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The Toyota recalls to date have focused on sticky accelerator pedals and so-called “carpet entrapment,” where loose floor mats could become tangled with accelerator pedals making it difficult to slow a vehicle down. The first recall, in October 2009, was triggered by a case in which an off-duty California Highway Patrol officer and several family members were killed when a Lexus he was driving raced out of control due to carpet entrapment.

Along with the recalls, Toyota has assigned key executives to new posts monitoring safety-related issues, but it has continued to face problems. While final data for 2013 hasn’t been compiled, the Japanese maker had more vehicles covered by recalls in the U.S. market during four of the previous five years than any other manufacturer.

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Just last month, Toyota ordered dealers to temporarily stop selling a wide range of products because of a defect related to their seat heaters. During an interview last week, Toyota’s second-ranking U.S. executive, Bob Carter, described the problem as “inconsequential,” though he also acknowledged that NHTSA may yet order the recall of vehicles already in the hands of consumers.

A settlement in the sudden acceleration case could be announced over the next few weeks, according to sources, though they caution a deal is not finalized yet. Along with the fine, Toyota would likely accept a deferred prosecution agreement putting it on probation for a number of years.

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“Toyota continues to cooperate with the U.S. Attorney’s Office in this matter,” company spokesman Ed Lewis said in a statement. “In the nearly four years since this inquiry began, we’ve made fundamental changes to become a more responsive, customer-focused organization, and we’re committed to continued improvements.”

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