"She said, hi, I'm good," her chief of staff, Pia Carusone, told the paper. He is the brother of Giffords' husband, astronaut Mark Kelly.
She has also been receiving bedside briefings from aides on the recent uprising in Egypt and on last week's decision by Republican Sen. Jon Kyl of Arizona not to seek re-election,
"We tell her everything that's going on," Carusone said. "Don't get the idea she's speaking in paragraphs, but she definitely understands what we're saying and she's verbalizing."
Giffords was shot in the head Jan. 8 while meeting with constituents outside a Tucson grocery store. Six people, including a 9-year-old girl and a federal judge, were killed in the attack, and 13 others, including Giffords, were wounded.
The congresswoman began intensive rehabilitation at TIRR Memorial Hermann in Houston late last month. The Times reported that an e-mail sent to friends about a week ago by Giffords' mother said that Giffords has been doing squats and repetitive motions to build her muscles and walking through the hospital's halls while holding onto a cart.
The 40-year-old Giffords has beaten one of her nurses at tic-tac-toe and has changed from "kind of a limp noodle" to someone who is "alert, sits up straight with good posture," the e-mail from Gloria Giffords said.
Doctors said in late January that they planned to insert a speaking valve into her tracheostomy -- a tube inserted into Giffords' throat to assist her breathing immediately after the shooting. Her doctors have not said whether that procedure took place or whether the tube was removed since she no longer needs it.
Rehabilitation specialists say brain injury patients who regain speech typically begin to do so about four to six weeks after the incident. Several news organizations reported last week that Giffords asked for toast with her breakfast one recent morning.