Earnest, after the discovery of the Genesis Apocryphon, there's a tendency to date the Aramaic portions much earlier. Here's some of the sources I looked up. Scholars were very careful not to contradict the mainstream beliefs on the dating of Daniel. They could lose their tenure if they tended to swim against the current. Would be interesting to find out what current thought is on the matter:
Most modern scholars prefer a late Maccabean dating (of around 165 BCE) for the book of Daniel in line with Driver’s famous assertion that “the Greek words demand, the Hebrew supports, and the Aramaic permits, a date after the conquest of Palestine by Alexander the Great (BC 332).”[1]
But already in 1965 Kitchen would take issue with Driver when he demonstrated a number of linguistic features that could indicate an earlier date for the stories.[2] Fitzmyer on the Genesis Apocryphon also points to an earlier date for the Aramaic of Daniel.[3] Coxon was cautious in his series of linguistic studies in the late 1970s but allowed that much of the evidence could point to an earlier date for the Aramaic of Daniel.[4] Other work, by such as Yamauchi and Masson, casts doubt on the particular notion that the presence of Greek words in Daniel necessitates a late date.[5] More recently Z. Stefanovic, The Aramaic of Daniel, p. 108, concludes that ‘the search for features in (Daniel Aramaic) of an early date should be pursued more intensively.’[6]
John J. Collins, a staunch defender of a late date Daniel, discredits the work of Stefanovic in no uncertain terms, yet he makes an unusual concession. While acknowledging that a “precise dating on linguistic grounds is not possible,” he concludes that the Aramaic of Daniel is later than that of the Samaria papyri (Wadi Daliyeh, fourth century BCE) but earlier than that of the Genesis Apocryphon (1Q20).[7]
E. C. Lucas proposes: “The form of the prophecies of Dan. 8:23-25 and 11 is best explained if they originated in the Babylonian Dispersion and the author was well acquainted with the Babylonian omen literature, someone skilled in the language and letters of the Chaldeans, as the account in Dan. 1 indicates.”[8] However, in line with what Collins said, if the “Men of the Great Synagogue” did indeed edit parts of Daniel, as the Talmud suggests, then a precise dating of the book on linguistic grounds would be impossible.
[1] S. R. Driver, Daniel, p. lxiii. See also A. A. Bevan, Daniel, pp. 41, 42.
[2] See his conclusions in K. A. Kitchen, ‘The Aramaic of Daniel,’ in D. J. Wiseman et al., Notes on Some Problems in the Book of Daniel (London: Tyndale Press, 1965), pp. 77–79. A much earlier move in the same direction was taken by H. H. Schaeder, Iranische Beiträge (Halle: Max Niemeyer Verlag, 1930), I, pp. 199, 120, as cited by P. A. David, ‘The Composition and Structure of the Book of Daniel: A Synchronic and Diachronic Reading,’ under ‘Composition and Structure,’ p. 50.
[3] J. A. Fitzmyer, ‘Some Observations on the Genesis Apocryphon,’ CBQ 22 (1960), p. 279; and Genesis Apocryphon, pp. 19–23. See also G. L. Archer, ‘The Aramaic of the “Genesis Apocryphon” Compared with the Aramaic of Daniel,’ in J. B. Payne (ed.), New Perspectives on the Old Testament (Waco, TX: Word Books, 1970), pp. 161–169, whose polemical tone should not distract the reader from his argument for Daniel Aramaic as an early eastern form of the language.
[4] For example P. W. Coxon, ‘A Morphological Study of the h-Prefix in Biblical Aramaic,’ JAOS 98 (1978), p. 416; ‘The Problem of Consonantal Mutations in Biblical Aramaic,’ ZDMG 129 (1979), p. 22; ‘The Distribution of Synonyms in Biblical Aramaic in the Light of Official Aramaic and the Aramaic of Qumran,’ RevQ 19 (1978), p. 512; and ‘The Syntax of the Aramaic of Daniel: A Dialectical Study,’ HUCA 48 (1977), p. 122.
[5] E. Masson, Recherches sur les plus anciens emprunts sémitiques en grec (Paris: C. Klincksieck, 1967), pp. 113, 14; and E.M. Yamauchi, ‘Daniel and Contacts between the Aegean and the Near East before Alexander,’ EvQ 53 (1981), p. 47, who concludes his essay with the hope that ‘future commentaries will come to recognize that the Greek words in Daniel cannot be used to date the book to the Hellenistic age.’
[6] T. J. Meadowcroft, (1995). Vol. 198: Aramaic Daniel and Greek Daniel: A Literary Comparison. Journal for the Study of the Old Testament Supplement Series, pp. 277–278. Sheffield: Sheffield Academic Press.
[7] John J. Collins, A Commentary on the Book of Daniel, Hermeneia-series, pp. 16 [footnote 156], 17, and R. J. Korner, “The “Exilic” Prophecy of Daniel 7: Does It Reflect Late Pre-Maccabean or Early Hellenistic Historiography?” in Prophets, Prophecy, and Ancient Israelite Historiography [ed. M. J. Boda and L. M. Wray Beal; Leiden: Brill, 2013], p. 348.
[8] E. C. Lucas, “Daniel: Resolving the Enigma,” Vetus Testamentum, Vol. 50, Fasc. 1 (Jan., 2000), p. 76.