A three-time Pro Bowler, Pouncey started 93 games in seven seasons with the Dolphins and played in all 16 games last season for the first time since 2012.
Pouncey, 28, was signed through the 2020 season as part of a five-year contract extension with the Dolphins in 2015. With his release, the Dolphins saved $7 million on their salary cap.
Pouncey told the Palm Beach Post on Thursday that he wanted a raise, but the request was declined.
The Chargers could use help up front on their offensive line and have not found a long-term replacement at the center position since Nick Hardwick retired after the 2014 season.
Spencer Pulley started all 16 games last season in his first year as a starter, but the Vanderbilt product's performance was uneven.
If the Chargers sign Pouncey, they would have a projected starting offensive line of Russell Okung at left tackle, Dan Feeney at left guard, Pouncey at center, Forrest Lamp at right guard and Joe Barksdale at right tackle.