The source confirmed that the federal government believed Loughner was now competent to stand trial and will argue that in court on Tuesday. Loughner is willing to change his plea to guilty at the previously scheduled hearing, the source said.
Psychiatric experts who have examined Loughner were scheduled to testify in a mental competency hearing on Tuesday that he was competent to stand trial and understood the 49 charges against him, the Los Angeles Times reported earlier.
A spokesman for the U.S. Attorney's office in Phoenix said he could "neither confirm nor deny" whether Loughner would plead guilty.
The team of four attorneys representing Loughner had not responded to emailed requests for comment.
Giffords, an Arizona Democrat seen as a rising star in the party, was holding one of her regular "Congress On Your Corner" events at a Tucson supermarket in January 2011 when she was shot through the head at close range by a gunman who killed six other people, including a federal judge and a 9-year-old girl.
Loughner, 23, is charged with 49 criminal offenses including first-degree murder over the shooting rampage, which wounded 13 people. A not guilty plea was entered on his behalf last year.
The Wall Street Journal, which also reported that Loughner would plead guilty, said Tuesday's mental status hearing had been changed to a change-of-plea hearing, citing an official familiar with the case.
If U.S. District Judge Larry Burns were to determine at Tuesday's hearing that he was fit for trial, Loughner - who is being forcibly medicated to treat his psychosis - could face the death penalty if found guilty.
The Los Angeles Times said it was unclear on the details of the plea arrangement, or whether Loughner would plead guilty to all or just some of the charges in exchange for prison time rather than risk being sentenced to death at trial.
Tuesday's hearing was to be Loughner's fourth to determine if he is fit to stand trial. Burns ordered the hearing in June at the request of prosecutors and defense attorneys who wanted a status report after more than a year of treatment and legal wrangling over his mental competency. The college dropout was determined unfit for trial in May 2011 after experts said he suffered from schizophrenia, disordered thinking and delusions. Loughner has been held at a U.S. Bureau of Prisons psychiatric hospital in Springfield, Missouri, where he is forcibly medicated against his will to treat psychosis and make him fit for trial. Giffords resigned from the U.S. House of Representatives in January to focus on her recovery. Her former aide Ron Barber won a special election to fill her seat and will have to win re-election in November to serve a full two-year term.