The Twins are likely to carry five infielders. Morneau is set at first base and Gardenhire has apparently abandoned any idea of competition at third by making Plouffe his third baseman. So the competition is really for three spots in the middle infield, second base, shortstop and utility infielder.
Because Carroll can play all three infield positions, it isn't necessarily essential that the utility infielder play shortstop if Carroll is the starting second baseman. Its also possible the Twins would carry a sixth infielder, which would give guys who do not profile as shortstops a better chance at making the roster.
I will update this list as spring training progresses.
Carroll (2b, ss, 3b)
Dozier (2b, ss)
Olmedo (2b, ss, 3b)
Beresford (2b, ss)