The infinitive not in indirect discourse has μή; the infinitive in indirect discourse has οὐ, but sometimes μή. The articular infinitive has μή. On the use with μὴ οὐ see cross2742 ff.
a. The ordinary negative of the infinitive is μή, which could be so used since the infinitive was employed as early as Homer in an imperative sense. οὐ with the infinitive in indirect discourse is probably due to the analogy of οὐ with the indicative and optative in clauses of indirect discourse introduced by ὅτι (ὡς). οὐ became the natural negative of indirect discourse as soon as the infinitive came to represent the indicative or optative.
Herbert Weir Smyth [n.d.], A Greek Grammar for Colleges; Machine readable text [info] [word count] [Smyth].