With Nathan a question mark, there are one or two positions open. I assume Liriano has all but won the fifth starter position. The other pitchers still in camp are Neshek, Duensing, Perkins, Manship, Slama, Waldrop and Maroth. The last three are not on the major league roster.
Neshek has done well in spring training but still has not got his velocity up to 90-mph. As I understand it, he still has options left and if he isn't throwing at full velocity, they are likely to send him to Rochester to work on his arm strength.
Gardy made a comment about Perkins getting his work in because he was going to "be a starter somewhere". I think the Twins still hope to move him, but if not he is likely going to get the sixth starter spot pitching at Rochester. He also still has options left.
Duensing is still competing (along with Perkins and Liriano) for the last starter spot. Since I think Liriano has won that competition, Duensing is likely to end up starting at Rochester. But if both Perkins and Duensing are still around one of them will likely be in the major league bullpen.
Manship has struggled so far in spring training. Unless he can step things up in his next couple outings, he will likely start the season at Rochester. If he improves and Perkins is moved, he might get a major league spot as the long reliever while Duensing is at Rochester keeping himself ready as a starter.
This leaves the three non-roster guys. I am not sure where the room is found for them, but I don't think that will be the decisive question in choosing bullpen spots.
Maroth has the advantage of being a major league veteran. With two spots open, it seems likely that will be an advantage. If Nathan (or an outside guy) is the closer, then filling the last spot with someone inexperienced may be less risky. Of course Maroth has to show he can get major league hitters out. He had a rough start to the spring, but obviously they still think he could help them or he wouldn't still be in camp.
Slama has been turning fans heads. Likewise, Waldrop has had good success. The two of them need to show they can continue that success as the competition improves the rest of spring training.
I would call Duensing and Maroth the favorites right now, but Slama and Waldrop have legitimate shots at spots. I don't think Gardy wants Perkins around and will find a way for that to happen whether by trade or sticking him at Rochester.
Couple recent posts elsewhere on the Twins bullpen situation: