The 30-year-old was part of the Jets' side that reached the AFC championship game in consecutive seasons in 2009 and 2010, but they failed to get to the Super Bowl on both occasions.
"Every year you're not in it, it stings. It's disappointing," Mangold told the New York Post. "A lot of my friends have rings, and I'd like to get one."
Mangold has played 126 games in the NFL and has been voted as an All-Pro three times in his career.