Releasing Brunell was among the Jets' first moves Friday morning as the team was in intense negotiations to try to reach an agreement with cornerback Nnamdi Asomugha. Several other teams are interested in the player considered to be this year's top free agent.
La Canfora also reported that New York also released quarterback Kevin O'Connell, according to a league source.
O'Connell spent last season on injured reserve after injuring his throwing shoulder. Drew Willy and seventh-round pick Greg McElroy, who agreed to a deal Friday, are the other quarterbacks on the roster.
The team announced earlier Friday it had waived cornerback Will Billingsley and guard Marlon Davis. Both were signed to reserve-future contracts by the Jets in January.
The Associated Press contributed to this report