Nietzsche's theory has many similarities with Callicles thought in Plato's Gorgias (Nietzsche and Callicles on Happiness, Pleasure, and Power). However, he did not explicitely mention Callicles in his writings. Did he acknowledge anywhere having read Gorgias dialogue?
I don’t know of a definitive reference. The book on the presocratic Greek philosophers may possibly have a reference to Callicles but I don’t believe so. Deleuze’s Nietzsche and Philosophy (on II.9) has some interesting remarks on their resemblance however, noting that Callicles is indeed a clear precursor to Nietzsche, and that Nietzsche may be understood as having “completed” Callicles.
Nietzsche was a philosopher as well as being well read in works of Ancient Greece. His first work after all was The Birth of Tragedy, a work of literary analysis on the form of tragedy in Ancient Greece.
He is also well known to see himself as sui generis and rarely refers to the work of other thinkers that influenced his thought. For example Darwin's notion of natural selection. Nor does he mention the Persian lyricism that informs his work, Thus Spoke Zarathrustha. So it is not surprising he doesn't mention Plato's work, Gorgias, specially considering his antipathy to Plato and Socrates.
The first professional philosopher to mention the parallels between the arguments of Callicles with those of Nietzsche is Adolph Menzel. In particular, Callicles argument that justice is born out of impotence and resentment antipates Nietzsche's notion of ressentiment.
This is mentioned in an essay by Bernardo Ferro on these parallels. In there he characterises the Nietzschean 'Will to Power' as a 'basic or primordorial' sense, which does not have an end, but is it's own end. This is reminiscent of Schopenhauer's notion of the Will behind all things. He also describes it as a 'physiological drive for self-enjoyment amd self-enhancement'. This 'physiology' separates it from Schopenhauer's account which is metaphysical and brings it into the biological and material world. But there it becomes self-refuting, for as the Buddha observed, people are born in weakness - they are born and end in weakness - they get old and frail!
I managed to find an explicit citation to Gorgias dialogue in his Homer's contest (it is written Georgias which is why it was not showing up), which shows he read it or at least was fully familiar with its content:
What, for example, in Plato is of special artistic significance in his dialogues is mainly the result of a rivalry with the art of orators, sophists, and dramatists of his time, invented for the purpose of enabling him to say at last: "Look, I too can do what my great rivals can; indeed, I can do it better than they. No Protagoras has written myths so beautiful as I, no dramatists created such an animated and fascinating whole as the Symposium, no orator composed such a speech as I put down in Gorgias - and now I reject it altogether and condemn all imitative art! Only the contest made me into a poet, into a sophist, into a orator!"
As a bonus, I emailed the Friedrich Nietzsche Society and they told me that most scholars who couple Nietzsche with Callicles are his detractors, because if one has a deeper understanding of his power ontology then most similarities are spurious and based on the well-known caricature of his thoughts. Interesting.