And on that second day, they have a linebacker in their sights.
The 27-year-old middle linebacker had a breakout season in Minnesota as 2012 was his first full season as a starter, making 97 total tackles with three forced fumbles.
The Giants could use an upgrade at the middle linebacker spot, especially with last year's starter Chase Blackburn now a free agent as well.
The team had been trying to bring Blackburn back for 2013, but he wanted to test the free agent market to see what was out there.
Brinkley was a fifth-round draft pick out of South Carolina by the Vikings in the 2009 NFL Draft and played mostly as a backup or on special teams before 2012.
This would be the kind of move that is very typical of Giants GM Jerry Reese.
Finding an up-and-coming player on the verge of breaking out—while under the radar—and being able to plug them into the starting lineup would be ideal.
Even if the Giants did manage to bring Blackburn back for another season, I think they should keep him on as a backup and for leadership, while Brinkley should be the starter.
It's no shock that the Giants are looking to upgrade their linebacker positions as well, considering the unit struggled in 2012, especially with injuries.
Aside from Blackburn being a free agent, Keith Rivers is also a free agent as well and Michael Boley was released back in February.
We'll have to see how this meeting between Brinkley and the Giants goes and if a contract offer is given at the end of it.
Stay tuned, Giants fans.