Let me know if you have any …………. news?

The adjective Far, changing to superlative and superlative, has two forms: farther/ farthest if indicating distance, and further/ furthest if indicating distance of knowledge or information.

=> In this case, B and D type, because the noun news (news)

The answer is A. This sentence uses the comparative.

Translation: If you hear any news, please let me know right away.