The man who once was believed to be the so-called "20th hijacker" in the Sept. 11, 2001, attacks (search) has told the federal government he plans to plead guilty to his role in the terrorist acts that left nearly 3,000 people dead, FOX News confirmed Tuesday.

The critical point, one source told FOX News, is whether Zacarias Moussaoui (search) is found to be mentally competent. If a judge finds that he is, he could enter the plea as early as this week. The source noted that nearly four years in solitary confinement may have taken a toll on the the French-Moroccan, who is the only person in the United States charged in connection with the 2001 attacks.

Frank Dunham, one of the court-appointed attorneys for Moussaoui, told FOX News that a hearing is scheduled for 11:30 a.m. Tuesday at the federal court in Alexandria, Va. Dunham said U.S. District Judge Leonie M. Brinkema (search) sent lawyers a letter on Monday indicating that she planned to assess whether Moussaoui is mentally competent to enter a guilty plea.

Moussaoui's attorneys have sent a letter to the judge indicating that at least one of them should be present during the assessment. This issue will be addressed in court on Tuesday.

The government accused Moussaoui of participating in an Al Qaeda (search) conspiracy to commit terrorism that included the 2001 attacks on the World Trade Center in New York and the Pentagon in Washington.

Click here for the Moussaoui case history (FindLaw).

Moussaoui has only confessed to being a member of Al Qaeda and pledging his loyalty to Usama bin Laden. Court observers believe that alone could be enough to send him to jail for the rest of his life.

The one-page letter to the judge and federal prosecutors in which Moussaoui, 36, apparently said he wants to plead guilty was sent from his jail cell two weeks ago. One source told FOX News that his wish to enter the plea and likely face the death penalty are against the advice of his attorneys. Sources told The Los Angeles Times that Moussaoui's lawyers wanted his request actually thrown out, arguing that it's his naive attempt to win a hearing before the U.S. Supreme Court.

But the high court last month declined to hear Moussaoui's appeal and it let stand a 4th U.S. Circuit Court of Appeals ruling that kept the death penalty in play and ordered a compromise on Moussaoui's access to top-ranking Al Qaeda figures that are in U.S. custody.

Contacted Monday night by The Associated Press and The Los Angeles Times, prosecutors and defense attorneys in the case declined to comment on the Post report.

Moussaoui tried to plead guilty in 2002 by claiming he knew intricate details of the plane hijackings. But he rescinded his plea a week later. His mental state has been an issue in the case ever since.

If Brinkema accepts a plea, she would then probably set a death penalty trial, at which jurors would decide if Moussaoui should be executed.

One source told FOX News that part of Moussaoui's motivation is that he may want to be a martyr for Al Qaeda. As for a timetable, legal sources would not comment, saying the case is currently under seal. It is unclear whether Brinkema may delay proceedings because she is so angry that sensitive information has been leaked to the press.

Moussaoui was indicted in December 2001, but his trial has been delayed three times.

The government has long believed that 20 people were meant to hijack the four jetliners on Sept. 11, although only 19 boarded the planes that morning. Moussaoui was first thought to be the possible 20th hijacker but prosecutors, along with the independent government commission that investigated the attacks, have dropped his name as the possible 20th person involved.

They now suggest that the Sept. 11 planners believed him too unstable to join the hijackers.

Moussaoui was arrested in August 2001 after a flight instructor in Minnesota alerted the FBI to what appeared to be suspicious behavior. He was in federal custody on immigration charges when the attacks occurred; after Sept. 11, he was indicted on six counts of conspiracy in the plot, four of which carry the death penalty.

His case is the only one related to the attacks that has come close to going to trial, and the Bush administration has viewed it as a key prize in its War on Terror, although it's been far from the slam-dunk case as originally anticipated.

Sources told The Los Angeles Times Monday night that Moussaoui's offer, on its face, would give the government what it wants — an execution.

"There will be no plea unless [the judge] knows for sure that he's serious and that it's going to go down like this," one source said.

FOX News' Catherine Herridge and The Associated Press contributed to this report.