It's probably in a soffit because it runs 90 degrees to the joists or joins up with ductwork that runs 90 degrees to the joists. If not, it may be possible to put it in the joist space if there are no other obstructions. You should be able to make the soffits shallower and flush with the cabinets. if you can't eliminate them altogether. But you can't tell until it's uncovered.

And you might be uncovering a nasty can of worms, I've seen some major problems with this type of thing on HGTV. I'd call in an expert for a realistic idea of what is there unless you have the original plans and know. It all looks very attractive the way it is. Seen from eye level few people will even notice the soffits.