Do dragons reincarnate in Westeros?

Question

I was browsing the Wiki of Ice and Fire, and found out this sentence:

Drogon is believed to be the reincarnation of Balerion the Black Dread, but Daenerys decides to give him a new name for his new life.

It references the passage where Daenerys names her dragons:

“Aegon’s dragons were named for the gods of Old Valyria,” she told her bloodriders one morning after a long night’s journey. “Visenya’s dragon was Vhagar, Rhaenys had Meraxes, and Aegon rode Balerion, the Black Dread. It was said that Vhagar’s breath was so hot that it could melt a knight’s armor and cook the man inside, that Meraxes swallowed horses whole, and Balerion . . . his fire was as black as his scales, his wings so vast that whole towns were swallowed up in their shadow when he passed overhead.”
The Dothraki looked at her hatchlings uneasily. The largest of her three was shiny black, his scales slashed with streaks of vivid scarlet to match his wings and horns. “Khaleesi,” Aggo murmured, “there sits Balerion, come again.”
“It may be as you say, blood of my blood,” Dany replied gravely, “but he shall have a new name for this new life. I would name them all for those the gods have taken. The green one shall be Rhaegal, for my valiant brother who died on the green banks of the Trident. The cream-and-gold I call Viserion. Viserys was cruel and weak and frightened, yet he was my brother still. His dragon will do what he could not.”
“And the black beast?” asked Ser Jorah Mormont.
“The black,” she said, “is Drogon.”
_{A Clash of Kings, Chapter 12, Daenerys I.}

By reading the statement that Drogon was considered a reincarnation of Balerion in its context, it seems that is it just something said because of the similitude of the appearance of Drogon to the likeness of Balerion, and nothing more. Also, the statement is from a Dothraki, hardly the most cultured people in the world.

But from Daenerys response, it is not very clear (at least to me) if she share this belief. From a certain point of view, it seems that she is trying to dismiss the notion without offending Aggo, on the other hand, she is replying "gravely" and explicitly states about a "new life", and maybe she is not entirely excluding the possibility of reincarnation.

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Regardless of Aggo and Daenerys opinions, this stirred my curiosity.
Are there more references in the published material (or in other semi-official statements from Martin) about this supposed reincarnation trait of dragons? This supposed "belief" that dragons reincarnate was just a one-time statement by Aggo, or there is some evidence that it is something broader?

Answer 1

It is unlikely that a dragon's "soul" is eternal or that Drogon is Balerion reincarnated.

I think we have to take this as metaphorical... Daenrys herself could be said to be "Aegon the Conquerer come again" as she is uniting the fractured Seven Kingdoms with three dragons.

In addition it is possible that Dany's eggs were even older than Balerion to begin with. Balerion was born roughly 400 years ago, lived for about 200, which but his death about 200 years ago.

When Magister Illyrio Mopatis gave her the eggs he stated:

"Dragon's eggs, from the Shadow Lands beyond Asshai," said Magister Illyrio. "The eons have turned them to stone, yet still they burn bright with beauty."

While a literal eon is one billion years, and the word is typically used in hyperbole, I would take it to mean more than 400 years, probably closer to a thousand years. I am not stating this as fact, but it does lend some context that dragons are unique to themselves.