ABC News in New York says Giffords and retired astronaut Mark Kelly will speak during the interview about a new initiative they're launching.
A call to a Giffords spokeswoman by the Associated Press wasn't immediately returned Sunday.
The interview by anchor Diane Sawyer will air at 6:30 p.m. Tuesday on 6abc.
Giffords and Kelly met Friday with the families of victims in last month's shooting in Connecticut that left 26 people dead inside an elementary school. The couple met earlier in the week with New York Mayor Michael Bloomberg, a longtime gun control advocate.
