Dakota Hudson, SP
Woodruff is a high-upside gamble who could replace Sonny Gray if everything works out, but the Twins would be lucky to find that kind of a needle in the haystack of non-tender players.
A much more realistic outcome is with a guy like Dakota Hudson. He's a former first round pick for hte St. Louis Cardinals who failed to pan out as part of the future there. He posted a 4.64 ERA across 221 innings the past two seasons, which was inflated from an already shaky start to his career with the Cardinals.
Hudson projects to be a back-end of the rotation starter, which makes him a perfect player to take a gamble on. Minnesota doesn't need him to replace Gray, but he could end up replaceing the other veteran pitcher expecter to exit in free agency: Kenta Maeda.
We have a pretty good idea of what the front of the rotation will look like next season, with Pablo Lopez and Joe Ryan being joined by 'Free Agent X' or someone the team trades Jorge Polanco and/or Max Kepler for (if not more). Guys like Bailey Ober, Louie Varland, and Simeon Woods Richardson are vying for that 4/5 spot in the rotation, and Hudson could give adequete competition for one of those two roles.