1.) The Twins have a real organizational dearth of MLB ready DH/1B types. Vargas, Palka and Byung Ho all don't seem to be in the long-term plans of the Twins at this point. Vargas seems the most likely but if this front office had any faith in Vargas, he'd have been on the team more consistently this year. Sano seems entrenched at 3B and Kepler isn't coming in from the OF. Robbie Grossman is a DH/OF but not a guy you hand the DH every day. After that, the only top 30 prospect at the position is Lewin Diaz and he's in low A ball. He's having a nice enough season but he's 3 years away if everything goes well. There's a lot of room at 1B/DH is my point - even if Vargas takes off he would likely DH. There's no internal option at 1B better than Joe.
2.) That means the Twins 1B in 2019 is likely to either be Mauer or come from outside the organization. I don't see the Twins spending big money in free agency (esp if they start locking down their young core) so the question becomes "Can you find someone better than Mauer when shopping at relative bargain prices?" I find that hard to believe, especially when you consider that Mauer still puts butts in seats in a way the James Loney types never could. Assuming Mauer is willing to take $5-$6 million a year for 2 years (I can't see him having much leverage, the only other place that makes sense for him is Tampa since he lives in FL?) he makes a lot of sense.
3.) The question then becomes, is Mauer good enough to be on the team? As others have pointed out, he’s not a prototypical first baseman, Not a lot of power. That said, he does bring things to the table. He’s become an elite defensive first baseman, particularly useful since the Twins have some subpar defensive options on the left side of the IF. His OBP is 40 points higher than average in total and eighty points higher against RHP. That’s a stat the Twins are short on. 1B isn’t where you usually get it but baseball isn’t a paint by numbers game. Mauer is definitely still a major leaguer.
4.) Mauer for the Twins in 2019 becomes more doable if you start thinking about a strict platoon. The Twins can either use Sano at 1B against lefties and put a better defender at 3B (they will likely have a surplus of SS at that point in time) or find the weak side of a platoon in free agency relatively cheaply (a Danny Valencia type who mashes left handed pitching isn’t going to cost more than $4 million). Either way, that gives you really nice 1B production for a fraction of the cost of a free agent stud.
5.) To me, the interesting part of the Mauer thing is going to be whether he wants to keep playing. He doesn't strike me as a guy who wants to chase records so that won't motivate him. He will have two daughters who are 4 years old so that will potentially pull him towards retirement. At the same time, he sat through a lot of bad Twins baseball and has to want to taste the upswing. He's never been a rah-rah leader so he'll be fine letting younger guys take the leading roles (has Joe Mauer ever wanted to do a postgame interview?). He seems to love the game and his body language playing is never down.
To answer the original question, assuming that Mauer wants to keep playing at the end of 2018, I put the odds of him being back with the Twins at 90%. He makes too much sense as part of a platoon for a 1B position that the Twins don't have a lot of other options for. He's not getting in the way of anyone's development, there's a ton of room at 1B/DH even if someone unforeseen comes into the organization, he's a big part of Twins history and his brother may be managing by 2019. There's no reason to think Mauer won't be a part of the team in 2019.