The Packers want Shields to return, but the 26-year-old instead will test the open market, according to the source.
A league source told ESPN.com earlier this week that talks had been "ongoing" between Shields and the Packers.
Shields, who played last season under a restricted free-agent tender of $2.023 million, is coming off his best season. He tied his career high with four interceptions in 14 games, including a game-changing pick in the fourth quarter of a Week 15 win over the Dallas Cowboys.
Last week at the NFL scouting combine in Indianapolis, Packers general manager Ted Thompson would not say whether the team would use the franchise tag on Shields if a deal couldn't be reached.
The deadline for teams to do so is Monday. The franchise tag for a cornerback is expected to be around $11 million this season.
ESPN.com Packers reporter Rob Demovsky contributed to this report.