"I will play again," Burress said in the interview with his former Steelers coach, Bill Cowher, scheduled to air on CBS' "NFL Today."
The interview was conducted from the upstate New York prison where the receiver is currently incarcerated after pleading guilty to attempted weapons possession in the second degree.
Burress said he works out about four times a week in the prison to keep in shape for a possible comeback.
"It's not LA Fitness or Bally's, but I do push-ups, sit-ups," Burress said in the interview. "I make do."
Burress was sentenced to two years in prison. He is expected to serve about 20 months with credit for good behavior -- meaning he could be released as early as spring 2011 -- followed by two years of probation.
Burress said he wrote a letter to Giants owners John Mara and Steve Tisch apologizing for his actions.
"I told them how sorry I was about bringing all this bad publicity to such a stand-up organization," Burress said in the interview with Cowher.
Burress, then with the Giants, was at the Latin Quarter nightclub in Manhattan in November 2008 with a .40-caliber gun tucked into the waistband of his track pants. He later said he was concerned for his safety because a teammate had been held up at gunpoint days before. The weapon slipped down Burress' leg and fired, injuring his right thigh.
The gun wasn't licensed in New York or New Jersey, where Burress lived, and his Florida concealed-weapons permit had expired. He also failed to report the incident to authorities.
Prosecutors argued the bullet narrowly missed a security guard, warranting a stiffer punishment. In early August 2009, Burress was indicted on two counts of criminal possession of a weapon and one count of reckless endangerment. He faced a minimum sentence of 3½ years if convicted at trial.
On Aug. 20, Burress pleaded guilty to a lesser charge and was sentenced to two years in prison.
Cowher, who was Burress' coach for five years in Pittsburgh, told the New York Post that he believed the receiver was sincere in the interview.
"He looked me in the eye. I believe he was sincere," Cowher told the newspaper. "I think I know him well enough to know that ...
"He admittedly blames no one except himself. He's had a lot of time to reflect. He's had great, unwavering support from his wife. ... It's been an eye-awakening situation for him. He had a daughter born when he was in prison. It's very sobering to be in there. When you walk through the door, and you listen to him talk, you can see it's very genuine."
Burress' work-release application was denied by the New York Department of Correctional Services last month because of the nature of his crime.
Burress became a Super Bowl hero when he caught the winning touchdown pass in the last minute of the Giants' 17-14 upset win over the previously unbeaten Patriots in Super Bowl XLII.
The Giants released him in April 2009.
Information from The Associated Press was used in this report.