A source told FOXSports.com that the Packers decided against using their franchise tag on Jennings, whose contract expired at the end of last season.
Green Bay had weighed doing so but such a move would have consumed $10.54 million of the team's $123 million salary cap. The Packers also have depth at the wide receiver position with Jordy Nelson, Randall Cobb and James Jones under contract.
Jennings, 29, was limited to eight games last season because of a groin injury. He became one of the NFL's most prolific wide receivers during his seven seasons in Green Bay and was especially productive in the deep passing game.
Jennings is considered one of the top wideouts set to hit the market when the free-agent signing period begins March 14.
The deadline for NFL teams to use the franchise tag is 4 p.m. ET on March 4.