are on pages 11 through 15 of Dave Remnick's article in the Jan. 27 The New Yorker (free online access): Annals of the Presidency: Going the Distance; On and off the road with Barack Obama. The article is the result of a lengthy "embed" with the president and ranges over the problems, both domestic and foreign, of his so-called "annus horribilus."
If you want to get the entire context of what he's thinking on the Mideast, read at least pages 11 through 15 (starting with the heading VI—A NEW EQUILIBRIUM, and not just the excerpted three paragraphs below, which I am copying only to give an idea of the detailed analysis that Remnick managed to get out of him:
[...] Ultimately, he envisages a new geopolitical equilibrium, one less turbulent than the current landscape of civil war, terror, and sectarian battle. “It would be profoundly in the interest of citizens throughout the region if Sunnis and Shias weren’t intent on killing each other,” he told me. “And although it would not solve the entire problem, if we were able to get Iran to operate in a responsible fashion—not funding terrorist organizations, not trying to stir up sectarian discontent in other countries, and not developing a nuclear weapon—you could see an equilibrium developing between Sunni, or predominantly Sunni, Gulf states and Iran in which there’s competition, perhaps suspicion, but not an active or proxy warfare.
“With respect to Israel, the interests of Israel in stability and security are actually very closely aligned with the interests of the Sunni states.” As Saudi and Israeli diplomats berate Obama in unison, his reaction is, essentially, Use that. “What’s preventing them from entering into even an informal alliance with at least normalized diplomatic relations is not that their interests are profoundly in conflict but the Palestinian issue, as well as a long history of anti-Semitism that’s developed over the course of decades there, and anti-Arab sentiment that’s increased inside of Israel based on seeing buses being blown up,” Obama said. “If you can start unwinding some of that, that creates a new equilibrium. And so I think each individual piece of the puzzle is meant to paint a picture in which conflicts and competition still exist in the region but that it is contained, it is expressed in ways that don’t exact such an enormous toll on the countries involved, and that allow us to work with functioning states to prevent extremists from emerging there.”
Obama’s lowest moments in the Middle East have involved his handling of Syria. Last summer, when I visited Za’atari, the biggest Syrian refugee camp in Jordan, one displaced person after another expressed anger and dismay at American inaction. In a later conversation, I asked Obama if he was haunted by Syria, and, though the mask of his equipoise rarely slips, an indignant expression crossed his face. “I am haunted by what’s happened,” he said. “I am not haunted by my decision not to engage in another Middle Eastern war. It is very difficult to imagine a scenario in which our involvement in Syria would have led to a better outcome, short of us being willing to undertake an effort in size and scope similar to what we did in Iraq. And when I hear people suggesting that somehow if we had just financed and armed the opposition earlier, that somehow Assad would be gone by now and we’d have a peaceful transition, it’s magical thinking." [....]
The full range is broader, including much more on Iran, and topics like drones in Yemen, al Qaeda, Egypt , Iraq etc.