An Arizona federal court has set a Tuesday hearing at which the man charged with wounding then-Rep. Gabrielle Giffords and murdering six others in a January 2011 shooting spree could plead guilty.

Arizona’s U.S. District Court is scheduled to hold a competency hearing Tuesday morning in Tucson, Ariz.

A scheduling order released by the court Monday says that if the judge finds Jared Lee Loughner competent to stand trial, then the court says it would entertain a change of plea at the request of Loughner’s lawyers.

“If the Court finds the defendant competent, his counsel has requested a follow-on change of plea hearing. Accordingly, assuming the Court finds the defendant competent, it will also consider whether to accept the defendant’s proffered pleas at the August 7 hearing,” the order says.

Larry Alan Burns, a federal judge in San Diego brought in to oversee the case in Arizona because one of the men killed, John M. Roll, was an Arizona federal judge, signed off on the scheduling announcement.

The Los Angeles Times reported Sunday that Loughner’s lawyers plan to enter a change of plea, but details were scarce on nature of the agreement.

A plea deal with federal prosecutors could potentially allow Loughner to avoid facing the federal death penalty in connection with the murders. He killed six and wounded 13, including Giffords, during the lawmaker’s “Congress on the Corner” event at a Safeway supermarket in Tucson.

In addition to Giffords, the wounded included current Rep. Ron Barber (D-Ariz.). Barber was working as Giffords’ district director and ran for the seat after Giffords resigned from the House in January to focus on her ongoing recovery.

Loughner reportedly now understands the nature of the charges against him and has expressed remorse for his actions. The Times says that medical professionals who have examined Loughner during his time in federal custody plan to testify Tuesday that he is now competent to face the charges against him.