The only reason the Blues would move Parayko is if they are landing someone else - namely Karlsson, Hamilton or Carlson. He's one of three RHD on the Blues roster (Pieterangelo and Bortuzzo).
Let's say the Blues get Karlsson. Then I can see them being interested in moving Parayko for futures. Parayko isn't all that much more valuable than Klefbom. So for me, that's probably a trade that could work - but wouldn't be possible until after July 1.
I'm also going to reiterate that if Barrett Haydon, Boqvist and Smith are there at no.10 - I hope like hell the Oilers take Hayton. He's being characterized by a lot of people as a 2nd / 3rd line center, but in my view he's a no.1 -2 down the line. A true two way player in the mold of Bergeron (someone tell me he's a no.2 C), Toews, Getzlaf, etc.