Drew Rosenhaus, who represents Shields, met face-to-face with the Packers with the hope the sides could work out a deal before Shields became a free agent on March 11, according to a league source.
No deal was completed, but the source described the negotiations as "ongoing." The sides are expected to be in regular communication over the next several weeks.
The 26-year-old 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 combine, 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 March 3. The franchise tag for a cornerback is expected to be around $11 million this season.
"I think Sam has been a good player for us, and he does a good job," Thompson said last week. "And he's one of the fellas we'd like to have back."