Is a runic manuscript of the Heimskringla realistic?

Question

In the story of Jules Verne's novel Voyage au Centre de la Terre, the protagonist acquires a very rare book: a copy of the Heimskrigla, the famous chronicle of the kings of Sweden written by the 13th century writer Snorri Sturluson. That manuscript copy is in the original Icelandic, written in the runic alphabet (futhark).

Is such a manuscript known in the real world? If not, is it realistically possible that such a manuscript existed? I'd have assumed all such codexes were written in the latin alphabet instead.

The following are quotes from the novel, chapter 2.

— Cet ouvrage ! répondit mon oncle en s’animant, c’est l’Heims-Kringla de Snorre Turleson, le fameux auteur islandais du douzième siècle ! C’est la Chronique des princes norvégiens qui régnèrent en Islande !

[…] Ceci est l’ouvrage original en langue islandaise, […]

[…] Mais, ignorant, c’est un manuscrit, et un manuscrit runique !…

[…]

« Les runes, reprit-il, étaient des caractères d’écriture usités autrefois en Islande, et, suivant la tradition, ils furent inventés par Odin lui-même ! […] »

Here are the quotes from an English translation, which can be found on Project Gutenberg: A Journey to the Interior of the Earth (1877) translated by Frederick Amadeus Malleson.

"This work," replied my uncle, firing up with renewed enthusiasm, "this work is the Heims Kringla of Snorre Turlleson, the most famous Icelandic author of the twelfth century! It is the chronicle of the Norwegian princes who ruled in Iceland."

[…] This is the Icelandic original, […]

"[…] It is a manuscript, a Runic manuscript."

[…]

"Runic characters were in use in Iceland in former ages. They were invented, it is said, by Odin himself. […]"

Answer 1

First: would a manuscript written in runes be plausible at all? Sure; the Scanian law, the first Scandinavian landskapslag to be written down, was in runic script.

Secondly: Were runes known on Iceland? Sure. The tradition of erecting rune stones never got there, so what we have are later manuscripts discussing runes, but this they did to a large degree. The knowledge about how to write runes were eventually lost to Danish and Swedish antiquarians, but were kept alive on Iceland (and among the people in mainland Scandinavia). An antiquarian as Snorri could reasonably be expected to know them.

Third: Did Snorri actually know runes? Unknown. According to Sturlunga saga, he was warned about the plot against his life in a letter written in what was likely some kind of cipher runes, but could not understand them. This does not prove that he could not understand ordinary runes; it might even be taken as a sign that the letter writer thought that he probably could.

Fourth: Do we know of any runic manuscript of Heimskringla? No. Do we know of any other icelandic manuscript written only in runes? No. Do we have reason to suppose that such a thing ever existed? No.

So, to answer the question: such a manuscript, while not totally impossible, is highly unlikely. However, there are certainly larger mistakes made by Verne in the text (Snorri was born in 1179, so he was more correctly a thirteenth century author, and the Heimskringla is mostly about Norwegian kings ruling Norway, with very little information about Iceland at all).