I've tried doing it from a saved swatch but it does not give me the library option in the swatch panel when I highlight that swatch.
You can’t save a gradient swatch to a CC Library, but you can save an object that is filled with the gradient to a Library. Create a shape, apply the gradient to the fill color, then add the graphic to the library.
In addition to what Theresa said; if you want also a gradient swatch in your Swatches panel, first create that swatch and then add the graphic with the gradient to the library.
That does not work very well.
This may not ever reach anyone but I really recommend Adobe to make it easier for gradients to be used through Libraries.
I'm having to open other Illustrator files to copy and paste the gradients over into new documents. It's a drag.
Why not add the feature?
We completely understand your concern. I would request you to please share a feature request here at our Adobe Illustrator Feedback form. This is the best way of communicating with the Engineering and Product Management teams regarding issues and suggestions so they can be implemented in future releases.
I you first save your gradient to your swatches panel, it will be automatically added there in new documents if you follow these steps.
Global colors, gradients and pattern swatches are not supported in CC libraries.
But as a workaround you can drag an object filled with a pattern/gradient/global color to the CC Library
You can also drag multiple items filled with different patterns/gradients/global colors together into a CC library to simulate a library.
The easiest way to add them to a new document is to hold down the Alt key when you drag them from the library and place them in a new document. The patterns/gradients/global colors automatically get added to your swatches panel.
You can hit escape before you click to place the object(s) or delete the dragged library items because the swatches are now part of the document.