Newman is a very dense read, and hence a very dense search. Unless you know for certain what search terms he’s using, or you find a very good index, you may as well just read the whole book. “Greeks” and “Orthodox” are prone to come up in many other contexts besides Greek Orthodoxy, for instance. So I’m very certain that I’ve read side comments along the lines above; but I have no idea where to find them.
There’s a bit in Apologia pro Vita Sua that says that initially, he figured that the Catholic Church had three branches: Roman, Greek, and Anglican, and that all three had inherited the whole of the Church.
There’s a bit in his conversion autobiography, Apologia pro Vita Sua, that glances at contemporary Orthodoxy, but not in an approving way. It’s in Part 5, “History of My Religious Opinions from 1839 to 1841”.
He recaps an argument article that he had written between two fictional arguers. One argues that the Catholic Church is the only catholic one, and that the others are cut off from the Vine, like St. Cyprian said of the Donatists. The other fictional disputant is recapped thusly:
“The other replies, by denying the fact that the present Roman communion is like St. Augustine’s Catholic Church, inasmuch as there are to be taken into account the large Anglican and Greek communions.”
Then there’s a lot more:
"As if all this were not enough, there came the affair of the Jerusalem Bishopric; and, with a brief mention of it, I shall conclude.
"I think I am right in saying that it had been long a desire with the Prussian Court to introduce Episcopacy into the new Evangelical Religion, which was intended in that country to embrace both the Lutheran and Calvinistic bodies… M. Bunsen and the then Archbishop of Canterbury were taking steps for its execution, by appointing and consecrating a Bishop for Jerusalem. Jerusalem, it would seem, was considered a safe place for the experiment; it was too far from Prussia to awaken the susceptibilities of any party at home; if the project failed, it failed without harm to any one; and, if it succeeded, it gave Protestantism a status in the East, which in association with the Monophysite or Jacobite and the Nestorian bodies, formed a political instrument for England, parallel to that which Russia had in the Greek Church and France in the Latin.
"Accordingly, in July 1841, full of the Anglican difficulty on the question of Catholicity, I thus spoke of the Jerusalem scheme in an Article in the British Critic: “When our thoughts turn to the East, instead of recollecting that there are Christian Churches there, we leave it to the Russians to take care of the Greeks, and the French to take care of the Romans, and we content ourselves with erecting a Protestant Church at Jerusalem, or with helping the Jews to rebuild their Temple there, or with becoming the august protectors of Nestorians, Monophysites, and all the heretics we can hear of, or with forming a league with the Mussulman against Greeks and Romans together.”
“…Now here, at the very time that the Anglican Bishops were directing their censure upon me for avowing an approach to the Catholic Church not closer than I believed the Anglican formularies would allow, they were on the other hand fraternizing, by their act or by their sufferance, with Protestant bodies, and allowing them to put themselves under an Anglican Bishop, without any renunciation of their errors or regard to the due reception of baptism and confirmation; while there was great reason to suppose that the said Bishop was intended to make converts from the orthodox Greeks, and the schismatical Oriental bodies, by means of the influence of England. This was the third blow, which finally shattered my faith in the Anglican Church. That Church was not only forbidding any sympathy or concurrence with the Church of Rome, but it actually was courting an intercommunion with Protestant Prussia and the heresy of the Orientals. The Anglican Church might have the Apostolical succession, as had the Monophysites; but such acts as were in progress led me to the gravest suspicion, not that it would soon cease to be a Church, but that, since the 16th century, it had never been a Church all along.”
He’s got a foreword from 1882, dealing with an Anglican man’s long attempt to get the Russian Orthodox Church to let him receive Communion. The gentleman left Newman his notes and papers on this attempt, so Newman learned Russian and published them as a book. (An unusual act of literary honor.)
Even in London, there simply wasn’t much going on with Orthodoxy in England. To go to any foreign immigrant church in a foreign tongue, even for reasons of church exploration, would have been highly unusual. That’s part of why Catholicism gave heebie-jeebies to Englishmen of Newman’s time. How much less likely would exploring Orthodoxy be?