The Cardinals have need for a quality back-of-the-rotation pitcher and both Harrell and Norris would likely be an upgrade from in-house options like Shelby Miller and Joe Kelly. Harrell is the younger of the two, at just 27 and with a career ERA of 3.93 in 235 innings pitched, he is also the better pitcher at this point. Norris has more than twice the experience with 563 innings under his belt, but his 4.42 ERA is below average, as is his 4.20 FIP.
While the Cardinals might prefer Harrell, Norris is far more likely to be available. Not only is Harrell younger and the better pitcher, but he is also less expensive. Norris is making $3M this season, his first arbitration-eligible year and he will become a free agent in 2016. Harrell is still two seasons from arbitration and will not reach free agency until 2018. The rebuilding Astros need players like Harrell to fill out their roster today at low cost and to potentially fill important roles in their next competitive team down the road.
If the Cardinals are looking to make trade, they almost certainly have the pieces to get a deal done.
The Astros are a long way from contention and so trading major-league talent for prospects is the name of the game for them at this point. Harrell might be hard to part with and carry a high asking price, but if they can get a reasonable return, Norris is exactly the type of player they would want to move.