He is making a statement about the growth of his nose, which depends on the statements he makes. Therefore the truth of his statement is indeterminate, making this a true paradox.

It can't be a true statement, because if it were, his nose would immediately grow and the statement would then become false. By the same token, it can't be a false statement, because if it was, his nose would immediately grow, thereby the statement would become true. But as any logician would tell you, a statement cannot "become" false when it was once true, or vice versa. Either it's true or false, or neither. In this case, it's neither.