Yes, absolutely. In his Historia Ecclesiastica (History of the Church), Sozomenus reports that Constantine first wanted to establish a second capital for the empire next to Ilium (the city the Ancients thougt to be mythical Troy, not that away from Schliemann's Troy). However, again according to Sozomenus, Constantine is said to have had a dream in which God commanded him to found his city on the Hellespont, and so Constantine, who had already ordered the contrusction of walls at Troy, changed his plans and established Constantinople in Byzantium instead. (Soz. 2, 3, 2-4)
Now there are a couple of problems with Sozomenus' report: Most importantly, of course, the supernatural elements. Sozomenus' perspective on history is a staunchly Christian one, and so he probably thought of Constantine's dream as a device to link the foundation of Constantinople, the second, Christian, Rome, directly to the Christian god. God(s) sending messages through dreams and thus shaping human history are, of course, a recurrent topos of ancient literature. Remember that according to Eusebius, the ☧-symbol was revealed to Constantine in a dream.
The other issue with Sozomenus' version is that it isn't confirmed by parallel tradition. Two other sources mentions Constantine's decision to rename Byzantium and to lavishly expand it: the Origo Constantini by the Anonymus Valesianus and Zosimus in his Historia nea. The second author gives a reason why Constantine decided to found a new city, but does not explain why the specific location of Byzantium was chosen.
So we're essentially reduced to look for circumstantial evidence to reconstruct the precise chain of events and Constantine's final decision. Earlier Roman rulers had already looked for a second city to conduct eastern (military) business from: Lucius Verus, who ruled the east while Marcus Aurelius reigned in the west, had opted for Antioch; as Augustus of the east, Diocletian had established his residence in Nicomedia in Asia Minor and planned to transform it into a "second Rome" (Demandt 2008, p. 22); even Constantine couldn't decide between Byzantium and four other cities: Serdica, Thessalonica, Chalcedon (directly opposite of Byzantium, in a much less advantageous geographic position as Byzantium) and, as mentionned above, Troy/Illium. (Demandt 2008, p. 357).
All of those cities had substantial advantages: Serdica and Thessalonica were on the Balkans, close both to Italy and to the Danube (one of the most important and militarized borders of the Roman Empire). The region was home to many of the military emperors of the 3rd and 4rd century CE, including Constantine's family. Chalcedon would, like Byzantium, have allowed for the control of the Hellespont and thus blocked the route from Europe to Asia Minor. Finally, Troy, while also controlling the approaches of the Hellespont and the traffic between the Mediterranean and Black Sea, had an obvious ideologic strongpoint: By establishing the empire's new capital at Ilium, Constantine would have come back to the mythical origins of Rome; every educated Roman knew the myth of Aeneas, the Trojan fleeing his home city and establishing a new Trojan homeland in the heart of Italy.
However, none of these arguments could beat Byzantium's almost perfect geostrategic position.
There's no real historical debate on why Constantine finally chose Byzantium as the location for his New Rome: It's easily defendable, and located between the Danube front on the Balkans and the Euphrates front in Mesopotamia. From there, both the Persian and the Gothic theaters of war were easily accesible. Constantine was familiar with the topographic situation at Byzantium: In his final conflict with Licinius, he had to besiege the city, which he finally captured in 324 CE; this must have been the moment when he realized how difficult it was to take the city without naval control of the Hellespont (which Constantine's fleet had previosuly achieved).
Primary Sources
Sozomenos, Kirchengeschichte, Erster Bd., transl. and ed. by Günther Christian Hansen (Fontes Christiani Bd. 73/1), Turnhout 2004.
Literature