They wouldn.t push him through the minors to be a 4th outfielder. By definition that would be someone who plays occasionally. By the end of next year they will need a firstbaseman who can hit and referably hit with power for a change. Be a run producer. The firstbase position should be opening up. Do we really want to put someone at a position that hasn't played there much in a couple of years? I don't think so. Therefore you move him to first.
A 4th OF does not by definition play occasionally. You know how I know that? The Twins 4th OF this year was Grossman and he played almost every day.
Rooker can be the 4th OF and play DH and 1B as well. No reason he can't be playing almost every day unless the Twins go out and get a big money 1B/DH type. That seems unlikely.
Mauer will be resigned. He's going to give a hometown discount and the Twins don't have anyone who needs to play 1B every day (they have DH open and Rooker can play OF) in the pipeline.
There's also no reason that 1B needs to be a run producer. That's outdated thinking. Guys are either MLB hitters or not. You try to put a lineup of the best hitters you can without screwing your defense. Mauer is an MLB hitter - who cares if his value is OBP instead of SLG? The Twins don't have a better player that they need to slot in at 1B.*
* All of this can change if they dip into free agency at the position. I just don't see that happening - doesn't seem like a Pohlad thing or a Flavey/Lavine thing. Especially since with Garver and Vargas and Rooker and Sano they may want some flexibility to use the 1B/DH in a more committee fashion. But I could be wrong - maybe they go get someone.**
** I don't love a lot of names on the list though. Carlos Santana is interesting but in a weak group, the years may be longer than expected. Pedro Alvarez is interesting but he bats lefty and doesn't fit well. From there you're in one-year guys like Mike Napoli, Jayson Werth or Bautista. No thanks.