In one of his many NFL Draft press conferences over the weekend, Scott Pioli noted that there would be some veteran players getting released with the new draft picks coming in. He wasn't talking about the Kansas City Chiefs, but about other players who will become free agents. He even said he didn't know what the "rumor mill" had let out already so obviously they're talking to some players.
Already we're seeing some veteran players getting the boot from their former teams. The Rams cut veteran kicker Josh Brown after drafting kicker Greg Zuerlein out of Missouri Western. The Redskins released Jabar Gaffney after trying to trade him during the draft. And other players will now start working out or signing with teams who didn't fill a particular position in the NFL Draft, like Vince Young visiting the Buffalo Bills.
The vast majority of what will be the 53-man roster is already on the team. But there will be some players hitting the market this week that could interest the Chiefs.
There's also the possibility that the Chiefs cut some of their own players now that they have their draft picks. The one we'll probably talk about quite a bit is Ryan Lilja, who has one year remaining on his deal and will see competition from 2nd round pick Jeff Allen.