SN44.10
“How is it now, Master Gotama, is there a self?”
When this was said, the Blessed One was silent.
…
“Why is it, venerable sir, that when the Blessed One was questioned by the wanderer Vacchagotta, he did not answer?”
“If, Ānanda, when I was asked by the wanderer Vacchagotta, ‘Is there a self?’ I had answered, ‘There is a self,’ this would have been siding with those ascetics and brahmins who are eternalists. And if, when I was asked by him, ‘Is there no self?’ I had answered, ‘There is no self,’ this would have been siding with those ascetics and brahmins who are annihilationists.
“If, Ānanda, when I was asked by the wanderer Vacchagotta, ‘Is there a self?’ I had answered, ‘There is a self,’ would this have been consistent on my part with the arising of the knowledge that ‘all phenomena are nonself’?”
“No, venerable sir.”
“And if, when I was asked by him, ‘Is there no self?’ I had answered, ‘There is no self,’ the wanderer Vacchagotta, already confused, would have fallen into even greater confusion, thinking, ‘It seems that the self I formerly had does not exist now.’”
AN6.38
“When there is an element of initiating, are initiating beings clearly discerned?”
“Just so, Venerable Sir.”
“So, brahmin, when there is the element of initiating, initiating beings are clearly discerned; of such beings, this is the self-doer, this, the other-doer.
SN22.99
“Suppose, bhikkhus, a dog tied up on a leash was bound to a strong post or pillar: it would just keep on running and revolving around that same post or pillar. So too, the uninstructed worldling … regards form as self … feeling as self … perception as self … volitional formations as self … consciousness as self…. He just keeps running and revolving around form, around feeling, around perception, around volitional formations, around consciousness. As he keeps on running and revolving around them, he is not freed from form, not freed from feeling, not freed from perception, not freed from volitional formations, not freed from consciousness. He is not freed from birth, aging, and death; not freed from sorrow, lamentation, pain, displeasure, and despair; not freed from suffering, I say.
“But the instructed noble disciple … does not regard form as self … nor feeling as self … nor perception as self … nor volitional formations as self … nor consciousness as self…. He no longer keeps running and revolving around form, around feeling, around perception, around volitional formations, around consciousness. As he no longer keeps running and revolving around them, he is freed from form, freed from feeling, freed from perception, freed from volitional formations, freed from consciousness. He is freed from birth, aging, and death; freed from sorrow, lamentation, pain, displeasure, and despair; freed from suffering, I say.”
SA33
”If it’s impermanent, it is suffering. It is a changing dhamma. Would the well-learned noble disciple in the middle way rather view: there is a self, there is other than self, both, or not?” The mendicants explained to the Awakened One, “Not at all, World Honoured One.”
“Mendicants, the well-learned noble disciple regarding these clinging aggregates, contemplate and examine them as they are: not self and not belonging to self. Having contemplated and examined them as they really are, they do not cling to anything that could be clung to in the world. Not clinging to anything that could be clung to they therefore do not hold onto anything. Not holding onto anything they therefore realise for themselves extinguishment.
My understanding is as follows:
All phenomena experienced by a sentient being are volitional constructs based on the fundamental delusion ‘I am’. Becoming conscious of its construct, it clings to its experience in a variety of ways… all of which ultimately lead to Rebirth and Suffering.
The way to break through this endless cycle- which is without discernable beginning - is to investigate the phenomena experienced and realize their Anicca, Dukkha and ultimately Anatta nature. This needs a calm, collected mind, which is where Sila and Samadhi come in.
Having seen through the illusory nature of all phenomena (even the very subtlest experienced in the formless meditations) - having let go of all constructing - the unborn, unchanging ultimately Empty nature of Everything becomes evident.
There never was anything permanent (viz Really Real) all along. It was its own conceiving, resting on the tripod of Namma/Rupa/Conciousness and originating with the volition ‘I am!’ that was the cause of the being’s Suffering.
At that point, the entire question of Is there a Self/ Is there no Self becomes pointless.
If at all there is to be an answer, IMO it could be “Having perceived X, identifying with X, delighting in X, not having understood the true nature of X a Self becomes apparent. Having directly known X, not identifying with X, not delighting in X, having understood its true nature, even the concept of Self can be let go of.”
Just my two bits… we all need to come to our own understanding in the end! Not to mention, actually walking the Path! 
Where did you learn about these pre-buddhist upanishadic references to atta? I think that is pretty useful to get closer to what Buddha meant by atta and anatta.
and other literature around it, but for the so inclined the original texts are quite interesting…
On the contrary, there are many texts which say what is Anatta viz what Atta is not. So, 