To be honest, the whole Arabic phrase here is cumbersome. (I have no news) or (I do not have news) is more like you're asking someone about something specific (like an update about something, or news about something) and they reply with this for "No."
However, if you are asking someone in the sense of (How are you: كيف حالك) or (what's new: ما الأخبار), then the answer would be something like (لا جديد: nothing new)