Build sooner or later...some time soon...maybe... So if there isn't a library existing now, and I haven't found any indication that there is, then what is Judicial Watch talking about?
https://www.obamalibrary.gov/about-us/frequently-asked-questions
The “library” may be digital, if I understand the link correctly.
They have been trying to build an Obama Center Illinois, but it is not a library? I do not get it.