There simply isn't a definition for it in the JLS. It just doesn't exist.
As for a weak reason, according to the JLS 14.3:
All local classes are inner classes (§8.1.3).
An interface can't be inner (JLS 8.1.3):
Member interfaces (§8.5) are implicitly static so they are never considered to be inner classes.
So we can't have a local interface.
This is, I guess, in addition to what @SotiriosDelimanolis has found that InterfaceDeclaration is not a BlockStatement.