Thomas' agent, Bus Cook, told NFL Network insider Jason La Canfora on Monday that the 10-year veteran has received inquiries from several teams already.
Thomas had 14.5 sacks in his three seasons in New England. But his lowest total came in 2009, when he had only three sacks.
He was a healthy scratch for the Patriots in two games last season, and was one of four players sent home by Belichick after arriving late for practice during a snowstorm in December.
While the three other players, wide receiver Randy Moss, defensive lineman Derrick Burgess and linebacker Gary Guyton largely remained quiet about the snowstorm incident, Thomas spoke out strongly the following day, saying he was "dumbfounded" and "can't figure out what Bill thinks or knows."
Thomas said he showed up nine minutes late for an 8 a.m. team meeting and had called ahead to say he was going to be late.
After being inactive in a 59-0 win over the Tennessee Titans in October, Thomas, asked by reporters why he was benched, said: "Ask Bill. He has all the answers."
Adalius Thomas, LB
Experience: 10 years
Thomas' departure leaves New England thin at outside linebacker, with Tully Banta-Cain the top returning veteran.
The Associated Press contributed to this report.