WOW that will require some $$$$$$ for sure that curve is going to require custom glass if you want to keep the light inside . Why enclose this I guess is my question?

Do you want to enclose the entire balcony area? What materials are you envisioning - all glass? Some glass?

I need more space and I hope the design will be a mixture of brick and glass.

You’ll need an architect

I assume you are not in the US but making that living space will requaire an architect with all the info needed where you live for doing what you want. I have no idea how big this space is but anything you put there to add living space will cut off natural light to the spaces you already have.

I would start by looking hard at how much useable space you'll get. Your balcony seems too narrow on the wings to provide much useable space. In the circular section, you have those two big columns. How many chairs would you be able to fit on the balcony when it is enclosed?

Next, you're probably going to end up with flat panes of glass in an octagonal shape. That's going to cut into the small floor space on the balcony.

I'm not an architect, but I suspect the cost is not going to be worth it.