There is no direct price. You Teleport it into your inventory, and then place it again when you want it.
Though I have not done it to test, I am sure you will lose the boost to your training size from the Breeding Ground. And, of course, you will not be able to produce orcs from it.
You should get back the population it is using, until you want to place it again, when you will need to have that population free.
I don't know if training size is taken into account for any formulas of other buildings. I can't think of any, but that doesn't mean none exist, so hopefully some others will weigh in.