Williams, who retired in 2000 after playing nine seasons in the NBA for the Philadelphia 76ers and New Jersey Nets, was to face a retrial in January on a reckless manslaughter count.
The person, who was not authorized to speak about the case, told the AP on condition of anonymity that Williams is to plead guilty Friday to aggravated assault. Because a gun was used in the crime, Williams must serve at least 18 months in prison, the person said.
Several messages left for defense attorney Joseph Hayden were not returned Thursday. The state attorney general's office, which has taken over the case, declined to comment on any aspect of the case because of a gag order.
The plea deal would resolve all charges in a case that dragged out for nearly eight years.
Witnesses testified that Williams was showing off a shotgun in his bedroom in February 2002 when he snapped the weapon shut and it fired one shot that struck driver Costas Christofi in the chest, killing him. They also testified that Williams initially placed the gun in the dead man's hands and instructed those present to lie about what happened.
The defense has maintained the shooting was an accident and that Williams panicked afterward.
During his trial, the jury deadlocked on the reckless manslaughter count, acquitted Williams of aggravated manslaughter and convicted him of covering up the shooting. He was never sentenced for the cover-up counts, pending the outcome of the retrial, and has remained free on bail.
The Star-Ledger of Newark was the first to report that a deal had been reached.
Williams had been offered pleas that would have called for him to serve less prison time, the person told the AP.
One of earlier offers, the person said, came just before a hearing last month on whether a racial slur used by a detective and other conduct by the county prosecutor's office should result in dismissal of the reckless manslaughter count and the cover-up convictions. State Superior Court Judge Edward Coleman later rejected the defense's claim that, had they known about the slur, they would have changed their trial strategy.