While specifically addressing a rumored trade between the Patriots and Cowboys, Adam Schefter mentions via Twitter that "there are any number of teams interested in moving back." While I'm sure there are teams looking to trade down, there always are, I could see why more teams might be interested than usual.
With so many potential free agents, and free agency coming after the draft instead of before it, there might be many teams interested in gathering extra draft picks to fill their roster spots. Just in case free agency doesn't work out for them. So I could see why the Cowboys might want to move down to grab an extra third or fourth round pick they could use to fill a spot somewhere else.
On the podcast earlier this week, I speculated that the wild free agency period might encourage some teams to move up in the draft. If every player with four years of service time is a free agent, for the Packers this would include players like LG Daryn Colledge and WR James Jones, then there might be a lot of quality mid-level free agents available. I could see some team aggressively moving up and willing to surrender a third or fourth round pick because they know they'll have a lot more options in free agency.
While there could be a couple of teams willing to gamble on free agency, I would expect that most teams are like the Cowboys. They're looking to trade down and draft players now, instead of waiting to see what happens in free agency.