Honestly, even if the Twins did agree to extend him, I really doubt they'd trade Buxton or Sano. One thing the Twins FO and ownership love, is to tout their homegrown talent. It's the one selling point they keep trying to use over and over with the fan base. From the days of Kirby, Herbie, Gaetti, Brunansky, etc...
While they historically have had a pretty good farm system, the one thing they don't have is an owner willing to take that last step and bring in a crucial piece via trade or free agency. Whether it's pitching or a bat. They either compete with what they grow themselves, or else. Gets tiring as a fan knowing they wont spend to push a decent team over the top. Only adding mid level or lower FAs. Look at their team from a few years ago. A consistent 90+ win team that kept winning their division, but weren't built to win in the post season. Looked good all year, then like complete ass come the short season. Ugh.