I follow a few undrafted free agents on Twitter and I've noticed a couple of these guys have been tweeting that teams are calling them. I didn't think teams were allowed to contact and sign undrafted free agents until Tuesday so I thought that was a little odd.
And then ESPN reported that, actually, the league gave teams the go ahead and talk to undrafted free agents on Monday night, which means the negotiations are underway right now. Teams can't sign these players until Tuesday at 10:00 a.m. (ET) but this gives everyone a head start.
This is actually a good move for the NFL, i think, because it gives teams some time to focus on undrafted free agent signings before things get really crazy the rest of the week. It'll also make for a busy night (and week) for general managers as they'll likely be working into the night.
Undrafted free agents can sign with any team, usually for the minimum, with varying signing bonuses.