You're trying to save money. Zaitsev is easily replaceable at his salary and value. Kadri is not.
He's really not... Not that we should be looking at either to clear salary, but we need Zaitsev more than we do Kadri, even though Kadri is a better player.
If we really get into a cap crunch, Gardiner is gone first. Easily number 1 on the chopping block. Hainsey is already moving out, and Marleau too soon after. If that ends up not being enough, then you start looking at guys like Brown. If that is still not enough, you either messed up or have too many core/high end depth players and you need to decide to move one of them... Which is when you can start talking about moving one of Nylander, Kadri or Zaitsev.
Matthews, Rielly, Andersen, Marner and Tavares are the only true untouchables. Kadri, Nylander and Zaitsev + some good value contracts (for now anyways) like Kapanen, Dermott and Hyman. After that, you either have good depth guys who are valuable but you can probably replace relatively easily(Ozhiganov, Leivo, Brown, Gauthier, Sparks, etc.) and the vets who will not be with the team for very long: Marleau, Gardiner, Lindholm and Hainsey.