CBS News correspondent Bob Orr reports that an examination of the computer has revealed Hasan visited Web sites promoting radical Islamic views, but investigators have not found any e-mail communications with outside facilitators or known terrorists.
One senior official told CBS News, "Everything continues to indicate that Hassan acted alone."
The official, though, said the investigation is "fluid and still in its early stages."
As part of a continuing background check the FBI is reviewing Hasan's actions and associations during his time in the Washington, D.C. area, where the psychiatrist worked at Walter Reed Army Medical Center.
Orr says that the FBI is aware of and is investigating reports (described in the London Telegraph) that in 2001 Hasan attended the same Virginia mosque as two of the 9/11 hijackers.
[The Telegraph does misstate that the Dar al-Hijrah Islamic Center is in Great Falls, Va., when it is actually in Falls Church.]
Investigators do not yet know if Hasan ever had an encounter with the hijackers Nawaf al-Hamzi and Hani Hanjour, but "... since all were in the area at the same time, it's possible," sources said.
More importantly, investigators are trying to determine what relationship, if any, Hasan developed with the radical Imam Anwar al-Awlaki, who was the spiritual leader of the mosque at the time. Even if Hasan had no direct relationship with al-Awlaki - a known extremist, now living in Yemen, who's been accused of aiding the 9/11 plot - investigators want to determine if al-Awlaki's teachings may have helped foster Hasan's radicalization.
"We need to look at potential inspiration" as a factor, sources said.
Officials say all of these potential leads, "need to be checked out before we attempt to attach any weight to them."
The FBI still has not interviewed Hasan, who was reportedly taken off a ventilator at the hospital where he is recovering, under guard, after being shot four times during Thursday's firefight.
More Coverage of the Tragedy at Fort Hood:
Army Says Hasan Taken off Ventilator
Fort Hood Suspect Said Methodical Goodbyes
Hasan Reportedly Felt U.S. Attacked Islam
Neighbor: Ft. Hood Suspect Packed Up Home
Hasan's Remarks Worried Muslim Leader