NASA said he has made his decision about whether to rejoin his shuttle crew and will announce it Friday. The news conference is scheduled for 2 p.m. at the Johnson Space Center in Houston (3 p.m. in Washington).
The Associated Press, citing an unidentified official close to the space program as its source, said Kelly has decided to go on the flight.
Giffords faces a long and uncertain path to recovery as she undergoes rehabilitation at a hospital in Houston, where Kelly lives. There have been no updates since Jan. 26, when Kelly announced that the hospital would be cutting back on reports to the public.
On Thursday, Kelly traveled to Washington to deliver a moving tribute to the power of faith during the National Prayer Breakfast. Remarking on his wife's steady improvement, he urged the nation to keep her in its prayers because "it's helping."
Kelly, a Navy captain, was invited to deliver the closing prayer for the annual event, which also featured President Obama. Kelly said the injured congresswoman continues to improve, but he did not offer specifics.
"Every day she gets a little bit better," he said. "The neurosurgeons and neurologists tell me that that's a great sign. The slope of that curve is very important."
Giffords was shot in the head Jan. 8 when a gunman opened fire during a constituent event in Tucson. Six people were killed and 12 others were wounded.
Kelly has been a consistent presence at Giffords's bedside and offered a glimpse of that experience on Thursday.
"I was telling Gabby just the other night, two nights ago, that, you know, maybe this event, this terrible event, maybe it was fate," he told the assembled dignitaries. "I hadn't been a big believer in fate until recently. I thought the world just spins and the clock just ticks and things happen for no particular reason."
He has come to believe "that maybe something good can come from all of this."
He did not say whether Giffords responded to his musings. A tracheal tube that has made it difficult to determine her ability to speak is scheduled to be removed soon.
Kelly mentioned a realization that struck him one day as he gazed on what he described as a "pilgrimage" site for the community, a collection of cards, flowers and candles that had sprung up in front of the Tucson trauma center where Giffords initially underwent treatment.
"That reminded me that you don't need a church, a temple or a mosque to pray," he said. "And prayer isn't just asking. It's also listening for answers, and expressing gratitude, which I've done a lot lately."
On Thursday, officials at University Medical Center in Tucson announced that volunteers will begin packing and archiving the Giffords tributes on Friday.