While the links found in the wikipedia entry of "Kraken" surprisingly do good jobs, how to identify/ to translate different terms in different language with the almost same entity can be problematic for this question, as is often with the case of such imaginary monsters.

The first undisputed and detailed reference of this monster with the name of "Kraken" is found at first in Natural History of Norway (Forsøg paa Norges naturlige Historie), authored by Bishop Eric Pontoppidan of Bergen, you can check the passages in question of old English translation (1755: Danish original is published in 1752) here.

Alternative scanned copy can also be found in: Biodiversity Library (linked to Pontoppidan 1755: 210)

A few early modern authors also mention the name of Kraken, and one of them, Hans Egede (the missionary re-discovered Greenland) writes an important annotation in his work, A Description of Greenland (1743 - linked to the rev. ed. of old English translation in 1818): According to Egede, Kraken is the same sort of sea monster appeared in Old Norse literature, called Hafgufa:

"This, though a very silly and absurd tale, is nevertheless matched by another story, every whit as ridiculous, told by my own countrymen, fishermen in the Northern part of Norway. They tell you, that a great ghastly sea monster now and then appears in the main sea, which they call Kracken, and is no doubt the same that the islanders call Hafgufa, of which we have spoken above. They say, that its body reaches several miles in length; and that it is most seen in a calm; when it comes out of the water, it seems to cover the whole surface of the sea, having many heads and a number of claws, with which it seizes all that comes in its way, as fishing boats with men and all, fishes and animals, and lets nothing escape; all which it draws down to the bottom of the sea. Moreover they tell you that all sorts of fishes flock together upon it, as upon a bank of the sea, and that many fishing boats come thither to catch fish, not suspecting that they lie upon such a dreadful monster, which they at last understand by the intangling of their hooks and angles in its body; which the monster feeling, rises softly from the bottom to the surface, and seizes them all; if in time they do not perceive him and prevent their destruction, which they may easily do, only calling it by its name, which it no sooner hears, but it sinks down again as softly as it did rise (Egede 1818 : 87, note 29)."

13th century Old Norse (Norwegian) text, called King's Mirror, also has a detailed passages on this Hafgufa, and the linked old translation employ the "Kraken" for the translation of "Hafgufa" (Larson trans. 1917: 125): https://archive.org/details/kingsmirrorspecu00konuuoft/page/124/mode/2up

While some experts still have little hesitation of translating Hafgufa as "Kraken" (Szabo 2008: 189f.), they are seldom mentioned in Old Norse literature (only 2-3 times) so that it is also not so easy to identify its characteristics.

The other references to Hafgufa, but almost primarily as a giant whale, is to be found in Ǫrvar-Odds saga (The saga of Arrow-Odd), legendary saga written in the late 13th century Iceland, though I cannot find its English translation online. A research points out the influence of the European scholary work, Physiologus, to its description of Hafgufa (Szabo 2008: 217f.).

Reference:

• Szabo, Vicki E. Monstrous Fishes and the Mead-Dark Sea: Whaling in the Medieval North Atlantic. Leiden: Brill, 2008.

(Edited): fixes typo (rather a mistake in copy & paste of the text, sorry).