Two general items up front: 1. Restricted free agents aren't real free agents. Anyone worth keeping will receive a high tender (1st and 3rd round, 1st round, or 2nd round picks as compensation) and it won't cause any salary cap problems in an uncapped year. "Teams have the leverage." Other NFL teams aren't going to offer a big contract and surrender a high draft pick. 2. The best thing the Green Bay Packers could do in free agency is resign all their current free agents.
This is category is the easiest one, and I'm lumping the Quarterback, Running Back, and Fullback positions into this one post.
Quarterback: I can't imagine them signing a veteran free agent QB of any shape or size. They might use a late round draft pick on a QB to develop and then stash on the practice squad for next season.
Running Back: RB Ahman Green is a free agent, but he wasn't signed until last October, and there appears to be little interest in him around the NFL. He might be resigned, but not until after the April draft. It's possible they might be looking for a new 3rd string RB to replace RB DeShawn Wynn and RB Kregg Lumpkin instead of resigning Green (or drafting a RB), but it would be a low cost move.
Fullback: Restricted free agent and starting FB John Kuhn received a low tender last February (no compensation if signed), and he still was resigned last April, so he's likely to draw little interest. Even if he isn't resigned, FB Quinn Johnson is the future, and the Packers should have little interest in other free agent fullbacks.