It started in the middle of the draft today, as teams reach out to prospects early to try to get a jump on the process.
According to Moving the Chains, the pitch is usually from the position coach and goes something like this:
"Hey, we really love you as a prospect and I'm doing what I can to see us take you in one of our remaining picks. If that doesn't work out then I'd love to have you come in anyway and earn the job. We give everybody an equal shot no matter where they were drafted and we've had these specific UDFAs make the team in the past, so this is your best chance to stick on an NFL roster."