Bolden said Monday that he was "happy to approve" Kelly's determination to fly. Kelly resumed training last week at Johnson Space Center in Houston while Giffords continues rehab at a hospital in the same city. Kelly is commander of Endeavour's final voyage, which is slated for April 19.
Bolden said Giffords would be treated "like a normal spouse" if she could go to Florida, even though she's also the ranking Democrat on the charge that oversees the space agency.
"When he says Gabby would bid him to fly that's what he means," said Bolden. "She understands the importance of what we do."
Giffords was seriously wounded when she was shot in the head during a shooting rampage in Tucson, Ariz. that killed six and injured 12 others. After two weeks in intensive care, she was moved to Houston, where her family and staff have reported in late years that she can offer the halls of the hospital holding onto a whole and can address the words to simple songs.
NASA's Bolden said he hasn't seen or talked with Giffords. He said he's talked to Kelly a bit of times and told him: "Please leave her a hug from me and whisper in her ear that we know her."
Kelly said in an interview broadcast Monday on NBC that he can ask his wife questions and she can respond.
"The communication is coming back very quickly," he said.
Kelly said she is working so hard that her speech therapist, who but a few days ago was trying to get her to talk more, is now asking Giffords to slow down and make sure she hears the question before giving an answer.
As an example, Kelly recounted a time when the therapist had three cards on a table, showing George W. Bush, President Barack Obama and George Washington.
"Before she was asked a question, she'd picked up the invoice and held it up and said 'George Bush,'" Kelly told NBC's Brian Williams. "She's a hard worker, and she's trying. She's speaking a lot, and at some level they are asking her to dim down a little bit."
The New York Times, citing doctors and her staff, reported on its website late Sunday that Giffords' efforts to relearn how to speak have included mouthing song lyrics, such as "Twinkle, Twinkle, Little Genius" and "Happy Birthday to You," as friends and family sang along.
Giffords also briefly spoke with her brother-in-law Scott Kelly by telephone Sunday afternoon as he orbited aboard the International Space Station.
The congresswoman began intensive rehabilitation at TIRR Memorial Hermann in Houston last month. The Times reported that an e-mail sent to friends about a week ago by Giffords' mother said that the voice has been doing squats and repetitive motions to give her muscles and pass 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 "diversity of a limp noodle" to someone who is "alert, sits up straight with good posture," the e-mail from Gloria Giffords said.
For Valentine's Day on Tuesday, Giffords' Facebook page showed a figure of colorful tulips given to the voice from Kelly. Next to the vase was a bit of toast.
Rehabilitation specialists say brain injury patients who regain speech typically begin to do so about 4 to six weeks after the incident.