At the crucial moment when the Babylonian wise men are forced to confront the king's highly unusual demand, the narrative undergoes a sudden linguistic shift into Aramaic. As the spoken language of the Chaldeans and the king himself, Aramaic becomes the primary language for most of the remaining story [אבן עזרא, מצודת ציון].
Among all the assembled advisors, the Chaldeans take the initiative to speak. As local experts in predicting the future, they consider themselves the most qualified to address the monarch [מצודת דוד, יוסף אבן יחיא]. Furthermore, unlike the foreign advisors at court, the Chaldeans are native to the region and completely fluent in Aramaic [מלבי״ם]. They deliberately choose to speak in a language that everyone in the palace can understand, hoping the public setting will make the king too embarrassed to insist on his illogical request [מצודת דוד].
They begin with the traditional royal greeting, wishing the king a long life. While this is standard court etiquette [מצודת דוד], it also carries a deep psychological purpose. The Chaldeans suspect that the king actually remembers his dream perfectly well but is terrified to share it, fearing it contains a dark prophecy about his own impending death. By emphatically blessing him with a long life, they attempt to calm his anxieties and coax him into revealing the vision [מלבי״ם].
Having set the stage, they ask the king to simply tell them the dream so they can provide its interpretation [רש״י, ביאור שטיינזלץ, מצודת ציון]. This request is based on their assumption that the king has not forgotten the dream but is merely seeking its meaning [אלשיך]. They explain that their wisdom requires basic raw material; once they are given the narrative of the dream, they can extract its meaning, but without that starting point, their task is impossible [יוסף אבן יחיא].
An alternative perspective suggests a more cunning strategy. According to this view, the Chaldeans claim they can uncover future decrees through astrology, but they cannot know the specific imagery the king's mind used to picture those events, such as whether a coming death was shown as a falling tree or a wild beast. Therefore, they propose that the king secretly whisper the dream to his other servants. The Chaldeans would then declare the interpretation without hearing the dream firsthand, supposedly proving their power. In reality, this is a calculated deception, designed to use trickery to retroactively fit their interpretation to whatever details of the dream might eventually be revealed [מלבי״ם].