Sources told the Houston Chronicle Dr. Dong Kim and a team at Memorial Hermann Hospital in Houston will attach a newly fabricated piece to protect the Arizona congresswoman's brain.
Surgeons at University Medical Center in Tucson had removed a large segment of her skull to relieve pressure caused by her swelling brain after she was shot in the head in a Tucson parking lot in January. She was one of 19 people shot; six died.
The Houston hospital has released no official report, but experts say the surgery should be quick with no complications, the Los Angeles Times reported.
The Chronicle said during the 1 1/2- to 2-hour procedure, surgeons will attach the implant with small titanium screws and plates. The piece will cover most of the left side of her head, currently covered by only skin and hair.
Giffords has been wearing a helmet to protect against injuries while she goes through rehabilitation.
On Monday, Giffords went to Florida to watch her husband, astronaut Mark Kelly, launch into space for the final mission of the space shuttle Endeavour. She returned to Texas Monday night.
Celebrity Families of 2014 [PHOTOS]