Presidential Libraries, while federal run cannot be built with federal money not on already designated federal land. To raise money for it, which must be entirely non-profit, is the responsibility of the outgoing President.
Between Trump being unable to admit he lost and not bothering to raise independent funds toward creating one, as well as the fact he was a one-term President, most Presidents only beginning the funding for one in their second term.
It is also probable that since Trump himself has plans to run for a second term, he has no desire to create an official archive. As well as the revenue that come from the library would only go back into maintaining it, in other words; a place to sink money into, Trump likely sees no point as he only views something as profitable if he personally gains.
He may still build one eventually or one may even be raised and funded once he passes away if he never tackles the issue and continues a never ending pursuit of a second term that may never come.
That isn’t to say there isn’t a library at all, albeit not a physical one. Much of Trump’s presidency was online anyway so of course those statements were preserved online on a server run by the NARA.
https://www.trumplibrary.gov/
