It is possible to have a small Assyrian country in the northern fringes of Iraq, with imposed expulsions of Assyrians into the country and likewise deportation of Turkmen, Kurds, Arabs, etc from their lands. Perhaps a Assyro-Armenian state therein. However, the state would not compose Mosul (Ninevah) most likely and it will be very rural in population and weaker than its neighbors. Though had the European powers been more interested in a large scale balkanization of the Mid East, it may be possible for the Assyrians to gain some more. This however would be anachronistic, as the European powers were not interested in these sorts of missions; had they been, there would at least have been a major Kurdish state carved near this hypothetical Assyrian state.
This is all somewhat naught however. The Assyrians of today and in 1919-1920, are a group of mixed populations who survived the destruction wrought by wars from 633-565 BCE within Assyria, that destroyed most major high cultural institutions in the region and a gradual displacement of its population by Aramaen Western Semites (already a large contingent) and varied Indo-European movements on its eastern and northern fringes. As a word, this may be called Aramaization of the remaining population, destroyed in their cities, bereft of their kings and likely the entire nobility, generalships and scribes slain between 615-607 BCE, the region of Assyria was left with its 'underclass' of a mass of peoples who had been deported there in the prior three centuries, mostly Western Semites and Elamites. Compounding this issue, the populace was ruled by the Achaemenid empire, who within Assyria, utilized Aramaic as opposed to the Akkadian high custom of Assyria (yet in Babylon, the Achaemenid standard included Akkadian as the highest formality; suggesting correctly the more continued prowess of Akkadian literature and speech within Babylonia than in Assyria).
Hence, at no point, do we see the return to Assyrian ruling motifs and the chronicles of Assyria never return to use, (Assyrian records cease speaking to us after 631 BCE, the proposed defeat of Assurbanipal against the Scythians) and all information we know of Assyria later is from non-Assyrians, especially the Babylonian chronicles that continue into the Seleucid era. Though, the Babylonian rulers show utter contempt towards the remains of Assyria, destroying the temples across Babylonian ruled Assyria. In Kalhu, the temple and great statues of Ninurta, the Great Warrior (despite being a Great God to Babylonians) was destroyed, alongside the temples to the Great Gods in Assur and other areas. Spared from this anti-Assyrian madness, was the city of Harran, which remained an Akkadian speaking city with an Aramaic lingua franca.
So, my opinion, would be the latest a true Assyrian state could arise, would be if a particular ruler taking a liking to Harran, becomes part of its social fabric, makes it his capitol and expands his power and conquers Assyria once more and drawing from the Harran memory, begins to affirm Assyro-Akkadian motifs. Nabonidus may have been in the process of this, he was a Shuprian (land Harran is located) king of Babylonia and was steadily moving the regime away from traditional Babylonian ruling motifs.
