You can only get so close to the look. A standard slide in fridge requires certain clearances for air flow and door swing/operation. This varies according to the fridge model so you will need to check out the specs.

Graham

I do this all the time with counter depth fridges and pantry cabinets . If you have the space the Electrolux all fridge / all freezer with builtin kit is awesome I have them in my home and in a few clients homes too with pantry cabinets built all around

If you mean covering the doors, then I can't imagine how you could do that -- the door panels that make the fridge disappear are really what the cost is about. However, if you just want to see a bit less of the fridge, you can do what I do in most of my renos, which is put full-depth panels on both sides of the fridge, and then pull the cabinet above forward to meet them. Yes, it's all deeper than the surrounding base cabinets, but it looks enclosed and clean.

You can also see whether your contractors can buy you a couple of inches of depth by framing the wall behind the fridge to partly recess it -- that can help make it less of a monster too.