The person, speaking about upcoming events in the case, said the plan is for Loughner to enter a guilty plea in the murders and attempted murders. The plan is contingent on the judge in the case allowing Loughner to enter the plea.
The Los Angeles Times reported earlier Saturday that Loughner was set to change his plea.
Bill Solomon, a spokesman for the U.S. attorney's office, said he could not comment on Loughner's case and the possibility of a guilty plea.
The Pima County attorney's office, which has said it could also pursue state prosecution of Loughner, declined to comment, said spokeswoman Isabel Burruel Smutzer.
Loughner had pleaded not guilty to 49 federal charges stemming from the Jan. 8, 2011, shooting outside a Tucson supermarket where Giffords was holding a meet-and-greet with constituents.
Authorities said he shot Giffords, opened fire on the crowd and was subdued by bystanders. Giffords was shot in the head and subsequently left Congress to devote her time to rehabilitation.
Giffords and her husband were traveling in Europe, and spokeswoman Hayley Zachary said Saturday she had no information on developments in Loughner's case.
U.S. Rep. Ron Barber, a Democrat who was elected in June to replace Giffords in Congress after she resigned, also was wounded in the shooting. A spokesman for Barber did not immediately respond to requests for comment.
U.S. District Judge Larry Burns ruled previously that Loughner isn't psychologically fit to stand trial, but that he could eventually be made ready for trial after treatment.
An Arizona college that Loughner attended released numerous emails about him that painted a picture of a struggling student with emotional problems who disturbed others with his strange behavior.
Experts have concluded that Loughner suffers from schizophrenia, and prison officials in Missouri, where Loughner has been held, have forcibly medicated him with psychotropic drugs.
Even though psychologists have said Loughner's condition is improving, his lawyers have vigorously fought the government's efforts to medicate him.
At one point, a federal appeals court halted the forced medication, but resumed it once mental health experts at the prison concluded that Loughner's condition was deteriorating further.
Loughner has demonstrated bizarre behavior since his arrest.
He was removed from a May 25, 2011, court hearing when he lowered his head to within inches of the courtroom table, then lifted his head and began a loud and angry rant.
His psychologist has said that since Loughner has been forcibly medicated, his condition has improved. He sat still and expressionless for seven hours at a hearing in September 2011.
Pete Yost reported from Washington.