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Kansas City Royals
The much-maligned Royals haven't had the season they anticipated. Their young players haven't developed the way they planned, particularly their pitchers. The Royals are very much in sell mode as they search for prospects to beef up their farm system. Controllable major leaguers are also in their sights. Carlson would fill the second void for them.
The Royals have MJ Melendez (73 OPS+), Kyle Isbel (68 OPS+), and Drew Waters (79 OPS+) currently roaming the grass; Dylan presents an immediate upgrade at any of the three outfield spots. His offensive numbers are much better than any of the three the Royals are fielding at the moment.
The Royals don't have much in the farm system that would be attractive to the Cardinals. They do, however, have some interesting rotation pieces that could be had for a fair price. Kris Bubic would have been an interesting return for Carlson, but he's currently injured. There is one more pitcher that could be had: Brady Singer. He is their "ace", but I'm sure the Royals would be willing to part with him for the right player in exchange.
Prediction: Dylan Carlson to the Royals, Brady Singer to the Cardinals.