First off, I highly doubt Liriano is going to sign an extension right now unless the Twins are going to overpay by a lot. Liriano is 2 months away from free agency and things have suddenly clicked for him. Unless Grienke implodes, Liriano is going to be in demand, even with the question marks.
Second, given his inconsistency, I'd be willing to go low base/high incentives with him. I doubt he and his agent would take it.
Third, Liriano has been kind enough of late to drive up his value. The Twins should be able to get something decent, and if they do not, they can make a qualifying arb offer and get a pick when he says no to arb. Not bad. I'd much rather flip that to a desparate team looking for pitching help and get a front line starter potential guy who is scuffling a bit in AA.
I'll be honest that I'm a bit skeptical of a long term contract for Liriano. I think he needs a change of scenery personally, and I wouldn't be surprised at all if he becomes "the one that got away." But given the headache and the frustration he's caused, I'd much rather sell while there is some value there.