"This man will not go to sleep."
Translation:यह आदमी सोने नहीं जायेगा।
That sentence would not be out of place in colloquial Hindi but in formal/written Hindi, the नहीं is placed adjacent to a verb (usually before the verb but can sometimes go after it for emphasis).
Coming to this sentence, सोने is no doubt a verb. However, it is used in the infinitive form which means it is acting like a noun (just like 'to sleep' in the English sentence).
So, place the नहीं next to जायेगा which is the main verb.