It is neither true nor false because it is begging the question.
sources:
True or false can only be applied to a question which has logical sense. Logic requires multiple statements and it is our desire to keep a consistency between the meaning of multiple statements which defines logic. Sometimes even though only one statement is presented there are other statements implied. But in this case there is only a single statement and there are no hidden implications. So just like poetry, the statement is alogical and cannot be scored as true or false.
https://en.wiktionary.org/wiki/alogical
"this" don’t refer to "this statement is false", because "A = not A" is false. If you said it explicitly: P : "P is false", you get "P : "P is false"" is false.
Then the negation of "this statement", don’t imply the negation of "this statement is false".