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Caesar's contemporaries seemed to have reason to expect this kind of military action before the end of 44 BCE at least after his assassination, if not before it. Cicero (de Div., ii. 110) refers obliquely to a rumor spreading among the people that Caesar needed to be granted the title of king:
We Romans venerate the verses of the Sibyl who is said to have uttered them while in a frenzy. Recently there was a rumour, which was believed at the time, but turned out to be false, that one of the interpreters of those verses was going to declare in the Senate that, for our safety, the man whom we had as king in fact should be made king also in name.
This story is also told by Suetonius (Iul. 79.3):
Nay, more, the report had spread in various quarters that [Caesar] intended to move to Ilium or Alexandria, taking with him the resources of the state, draining Italy by levies, and leaving the charge of the city to his friends; also that at the next meeting of the Senate Lucius Cotta would announce as the decision of Fifteen, that inasmuch as it was written in the books of fate that the Parthians could be conquered only by a king, Caesar should be given that title.
Dio (xliv. 15, 3) also records this rumor of the Sibylline oracle and that the Parthians could only be conquered by a king. While all this points to evidence that the people knew of these rumors surrounding Caesar and that they may have expected a Parthian invasion by Caesar, scholars believe that this story, rather than being wholly true, gives the appearance of subsequently justifying the ultimate tyrannicide. (Townend 1983) (Indeed Dio's account goes so far as to claim that the conspirators in Caesar's assassination actually believed the rumor.)
The most detailed account of the Parthian project is described by Plutarch (Caes., 58.2-5). It's important to note, however, that Plutarch's writing, Parallel Lives, was called such as he published pairs of biographical works of one Greek and one Roman in one "book". Pairing Caesar with Alexander meant that Plutarch wanted the reader to draw comparanda between the two historical figures as the two lives were meant to be read together. (Pelling 1986; Stadter 1975)
Thus, many scholars believe that such an extravagant military programme, as detailed in Plutarch, was not so much an historical account of reality, as it was literary flourish on the part of Plutarch who paired Caesar's biography with the great conqueror Alexander. Scholars take as evidence for this point the fact that the date of Plutarch's composition is placed during the early second-century CE when Trajan had already conquered Dacia, established a Roman province there, and was planning an invasion of Parthian territory. Moreover, the lack of military forces in the east in 44 BCE, either in Cilicia or Syria, suggests that the Parthian expedition was eithermostly literary construction or not of paramount importance to Caesar. (McDermott, 1982/1983)
Sources:
Buszard, B. 2008. "Caesar's Ambition: A Combined Reading of Plutarch's Alexander-Caesar and Pyrrhus-Marius." TAPA 138: 185-215.
Cicero: De Senectute De Amicitia De Divinatione. With An English Translation. William Armistead Falconer. Cambridge. Harvard University Press; Cambridge, Mass., London, England. 1923.
McDermott, William C. 1982/1983. "Caesar's Projected Dacian-Parthian Expedition." Ancient Society 13/14: 223-231.
Pelling, C. B. R. 1986. "Synkrisis in Plutarch's Lives." In F. E. Brenk and I. Gallo, eds., Miscellanea Plutarchea: Atti del I convegno di studi su Plutarco (Roma, 23 novembre 1985), Quaderni del Giornale Filologico Ferrarese 8: 83-96. Ferrara.
Stadter, P. A. 1975. "Plutarch's Comparison of Pericles and Fabius Maximus." GRBS 16: 77-85. Reprinted in Scardigli, ed., 155-64. Oxford.
Suetonius: Vitae Caesarium. With An English Translation. J. C. Rolfe. Cambridge. Harvard University Press; Cambridge, Mass., London, England. 1913.
Townend, G. B. 1983. "A Clue to Caesar's Unfulfilled Intentions." Latomus, T. 42, 3: 601-606.