It's one of the favorite topics pre-draft for any team, and I have no doubt GM Steve Keim will be asked the question when he and coach Bruce Arians have their upcoming pre-draft press conference: What are the chances of trading up or back with that first-round pick, which is 29th overall?
(Of course, I expect an answer along the lines of, "We'll consider both those options, depending on what deals are out there.")
Given that the Cardinals already gave up their second-round pick in the Chandler Jones trade, however, I find it hard to believe there would be any trade up. Keim loves his draft picks, the Cardinals only have six right now, and to move up and give up yet another choice somewhere would seem to be cost-prohibitive (and also, I'm not sure there will be someone out there in the 24 or 25 range, which is probably about as far as the Cards would be able to maneuver without gutting the draft class.)
Trading down, though, that's completely different. At 29 -- just two picks from the end of the first round, thanks to the Patriots losing their choice in Deflategate -- moving back into the second round isn't a crazy thought. To move down a handful of spots and pick up, say, another fourth-round pick would be enticing (especially if, for example, there is a quarterback later on upon which the Cards might want to take a flier.)
There was talk about possibly trading up last year, to get a pass rusher, but in the end the Cardinals stayed put and took tackle D.J. Humphries. Two years ago, they traded down (from 20 to 27) with the Saints, taking linebacker Deone Bucannon and then snagging wide receiver Smokey Brown with the extra third-round pick.
It's impossible to know if it will happen. Too many variables that come from being on the clock need to be filled in: Who is still on the board, what team might want to move up to get someone, and whether the Cardinals are OK with giving up a chance at whomever might be left. It would be interesting, though, to come in April 28 for the first round and have the story that night be that the Cardinals don't have any players yet.