Giffords is speaking again while a patient at TIRR Memorial Hermann hospital in Houston, KHOU television reported, citing unnamed staff members.
She verbally requested toast as she was being fed a meal on Monday, according to the political journalism organization Politico.
Giffords' spokesman in Arizona, was not available to comment.
The Arizona lawmaker was shot in the head outside a grocery store in Tucson, Arizona, on January 8. Six people, including a federal judge, were killed and 12 others were wounded. Jared Loughner has been accused in the shootings.