Steve Jensen of Connecticut Lt. Gov. Nancy Wyman's office told CNN Giffords, who left Congress after being wounded in the head in the Tucson mass shooting two years go, has a "planned visit" to Newtown scheduled for Friday.
Jensen said if the visit takes place it will be off-limits to the media.
ABC News said Giffords would be accompanied by her husband, retired astronaut Mark Kelly. The couple met Wednesday with New York Mayor Michael Bloomberg, who has been pushing for stronger gun control laws.
Giffords and Mark Kelly have also campaigned for gun control, including calling for an assault weapons ban.
A young gunman killed his mother at their home, then 26 people, including 20 children, at Sandy Hook Elementary School in Newtown last month.
Giffords, who represented an Arizona congressional district, was one of 13 people wounded in the January 2011 shooting outside a Tucson supermarket that claimed six lives.