Barwin told Sirius XM NFL Radio that he's looking for something specific from a team looking to add him to its roster.
"We've had interest from a number of teams all offseason," Barwin said. "The offers I have, I think I'll make my decision before camp starts. I'm not going to go somewhere that I don't think can win a Super Bowl."
Barwin recorded 34 tackles and five sacks in 14 games for the Los Angeles Rams last season.
The 31-year-old was playing in his first year with the Rams after four seasons with the Philadelphia Eagles. He even admitted that he had conflicting emotions after watching the Eagles win the Super Bowl.
"I was in a weird state for a couple of days," Barwin said. "I was kind of bummed out that I wasn't part of it."
Barwin has 354 tackles and 54.5 sacks in 126 contests over a nine-year career that's included stops with the Houston Texans, Eagles and Rams.
He has six forced fumbles and four fumble recoveries during his career that began as a second-round pick by the Texans in the 2009 NFL Draft.