Thomas and his agent, Drew Rosenhaus, visited New England on Monday and will continue negotiations with the team. Thomas is scheduled to visit with the New Orleans Saints on Tuesday.
Thomas, a seven-time Pro Bowl linebacker and one of the most popular and productive players ever to wear a Dolphins uniform, was cut Thursday, the biggest move yet in Miami's massive rebuilding project.
Thomas missed most of last season because of concussions and migraines and was placed on injured reserve against his wishes in December because of nagging migraines, an aftereffect of an Oct. 21 car crash.
The move is the second major salary slash this week by the Dolphins, who went 1-15 last season and subsequently brought in Bill Parcells to lead there building.
Miami trimmed about $9 million in 2008 base salary on Monday, when it parted ways with quarterback Trent Green, wide receiver Marty Booker and seven other players. Thomas was slated to make just over $5.6 million in base salary this coming season.
Thomas led the Dolphins in tackles 10 times, is the franchise's all-time leader in that category by a wide margin, and his 168 games is the most by any Miami defensive player.
The Associated Press contributed to this report