Twins second baseman Brian Dozier is coming off a 2016 season in which he blasted 42 home runs and batted .268/.340/.546 (136 OPS+) in 155 games. Since Dozier is a veteran contributor signed to a reasonable long-term contract (he's owed $15 million through the 2018 season) and the Twins don't seem to be going anywhere fast, trade speculation seems inevitable.
On that front ...
Dozier, as a middle infielder with power locked up at below-market rates, indeed makes sense for a number of teams. While it's uncertain whether the Twins are willing to trade him, it's worth noting that a new front office is in place in Minnesota, and it's one that may take a more realistic view of the Twins' near-term outlook. That is to say, contention in 2017 is unlikely. Dozier, thanks to his productivity and the modest financial commitment involved, could also net the Twins a healthy return as opposed to being a straight salary dump.
As for Dozier's replacement in Minnesota in the event of a trade, in the absence of an external solution some mix of Eduardo Escobar and Danny Santana would likely hold down the position. Jorge Polanco can play second, but he's probably going to remain the regular at shortstop.