The Twins have a full 40-man roster at present and there appear to be some players in St. Paul and perhaps Wichita who could help this club. Also, they only have two catchers on their 40-man roster, so an injury to one of the catchers (even if the player doesn't go on the Injured List) would necessitate a 40-man move.
First, let me run down the players who could be reasonably considered for promotion: Mark Contreras, Jake Cave, Jermaine Palacios, Curtis Terry, Chance Cisco or Jose Godoy, Devin Smeltzer, Juan Minaya and probably a half dozen other pitchers and Austin Martin in Wichita (although he is off to a slow start). Others may play themselves into consideration as the year rolls along.
With 24 pitchers on the 40-man roster, it would figure that a pitcher or two could be taken off the 40-man roster. Candidate #1 IMHO is Chris Vallimont. He's 25 years old, only reached AA and hasn't been effective at that level. #2 is Cody Stashak, who was just activated and knocked around by the Red Sox yesterday. To me, he doesn't look like the same pitcher who debuted in 2019. He doesn't have above-average velocity and has had injury issues. #3 is Jhon Romero, who the Twins claimed from the Nationals. He's 27 and has worked a grand total of 7 major league innings. For the Twins, he has allowed six hits in three innings. #4 is Drew Strotman, being converted to relief at St. Paul. He's 25, hasn't made his MLB debut and has had control issues.
With teams cutting back to 13 pitchers, I would think there would be a decent chance that none of these guys would be claimed. I don't advocate a DFA for all of them, but if the Twins want to upgrade their active roster, they will need to clear space on the 40-man.