Can we build a green house around the tree?

A greenhouse is not a tree house.

Greenhouses usually need full sun exposure. A tree will shade it too much.

Also, if a tree branch falls, there goes your greenhouse.

And then there is the ventilation issue. How will you seal the air leakage between the greenhouse and the tree at the top of the greenhouse?

If you have the money, you can hire an arborist to come out and remove the tree and transplant it elsewhere. They use a funky looking big machine to do it.

Cheaper to build the greenhouse away from the tree.

The downside of building any structure around a tree is that you are blocking access to it, or making it difficult. If that tree needs pruning or topping in a few years, for instance, you won't be able to get at it with a simple ladder. It's going to take a truck with a cherry-picker extension, and that won't be cheap.

If it grows large, its roots will, too, and they may interfere with your greenhouse's floor. If it is indeed a berry tree of some kind, will you be able to harvest it from within a greenhouse? Can bees get at it to pollinate? What will you do to deal with falling petals after it flowers, or falling leaves in the fall?

It seems like it could be way cool, but overall probably isn't a great idea.