Gautam Buddha is said to talk about Self in his teachings later during third turning of wheel (or call it whatever). He said about the self like this which is Advaitic & in agreement with both Advait Vedanta & Kashmiri Shaivism -
"You, monks, should not thus cultivate the notion (samjna) of impermanence, suffering and non-Self, the notion of impurity and so forth, deeming them to be the true meaning [of the Dharma], as those people [searching in a pool for a radiant gem but foolishly grabbing hold of useless pebbles, mistaken for priceless treasure] did, each thinking that bits of brick, stones, grass and gravel were the jewel. You should train yourselves well in efficacious means. In every situation, constantly meditate upon [bhavana] the idea [samjna] of the Self, the idea of the Eternal, Bliss, and the Pure ... Those who, desirous of attaining Reality [tattva], meditatatively cultivate these ideas, namely, the ideas of the Self [atman], the Eternal, Bliss, and the Pure, will skilfully bring forth the jewel, just like that wise person [who obtained the genuine, priceless gem, rather than worthless detritus misperceived as the real thing.] - The Buddha, Chapter Three, "Grief",The Mahayana Mahaparinirvana Sutra
Now of course not all Buddhists accepts this and start interpreting it scholarly like different Vedanta teachers interprets Aham Brahmasmi to suit their ideology. But going by context & translation it seems he actually is talking about eternal, blissful, infinite Advaitic AtmA which becomes evident when we read whole chapter and its context. In fact, by this words the monks got disturbed because of conflicts the Gautam Budhha made with his earlier teachings (which is the part of 1st & 2nd turning of wheel). Then he explains why he had said so earlier (Read complete story & explanation here) -
"Know, O you Bhiksus! The same is the case with the Tathagata, the Alms-deserving, the All-Enlightened-One, the Unsurpassed Best Trainer, the Teacher-of-Heaven-and-Earth, the Buddha-World-Honoured One. He comes as a great Doctor and subdues all tirthikas and bad doctors. In the presence of kings and all people, he says: "I shall become the King of doctors and subdue tirthikas." Thus we say: "There is no self, no man, no being, no life, no nurturing, no knowing, none that does, and none that receives." O Bhiksus! Know that what the tirthikas say is like the case of a worm that eats upon [a piece of] wood, from which, by chance, there appears what looks like a letter. Because of this, the Tathagata teaches and says no-self. This is to adjust beings and because he is aware of the occasion. Such non-self is, as occasion arises, spoken of, and it is [also] said that there is the Self. This is as in the case of the learned Doctor, who knows well the medicinal and non-medicinal qualities of milk. It is not as with common mortals, who might measure the size of their own self. Common mortals and the ignorant may measure the size of their ownself and say, 'It is like the size of a thumb, like a mustard seed, or like the size of a mote.' When the Tathagata speaks of Self, in no case are things thus. That is why he says: 'All things have no Self.'
So, after realizing and experiencing directly by himself (not through scriptures/reading/intellectual-understanding) he said there was no-self to break the notions of self that people had then as people were considering non self as self because of wrong notions about the self (i.e They were giving size of souls which according to Gautam Buddha was a wrong notion & was a subject to criticism). And that self which people were considering as Self was not indeed a self - was a reason he said 'there is no self.'
But my questions is based on the bolder parts - which schools of thoughts during those time (400 BCE) gave the finite or atomic size of AtmA (which they claim to be atomic)? As far as I know other than Vaishnava Schools no Indian philosophy give finite or atomic size of Atma. But Vaishnavas schools were organized only after Ramanuja, Madhwa etc. So what were the schools at the time or before Gautam Buddha who gave the finite or atomic size of Atma?
Note: The questions Size of soul in Hinduism texts & What is the size of the soul according to the different Astika schools? are not at all duplicate of this. I am specifically asking about the schools which were present before Gautam Buddha (400 BC) who used to describe the finite or atomic size. I know Vaishnavas gave the finite size (which is atomic) of soul but it had happened very much after Gautam Buddha (400 BC).