Here's to hoping this thread won't degenerate into the usual slugfest over the state of Entente finances in 1917.
I've created more threads on the topic of WWI ending with a negotiated peace in 1916-17 than any AH.com member has a right to, and I can't make any absolute promises that I won't create more at some point. My thoughts have been heavily influenced by Philip Zelikow's book on Wilson's peace efforts, because he's the only recent author to cover the subject in any kind of depth. Various posters have raised good points, and I can't say that I have perfect responses to all of them. The issue is getting both sides to the point where they feel more comfortable gambling on Wilson's armistice proposal than whatever their plans are for 1917. Suffice to say, it's pretty bloody difficult. Is it "impossible"? Maybe, but I would like to believe there was a chance.
The simplest POD is Wilson's December peace proposal having some actual teeth to it, stating some actual preconditions for an armistice, pending a proper treaty. Minimal conditions might be something like Germany restoring Belgium - Bethmann was okay with this, and if he get the Kaiser to agree to it, he can probably get it to happen - with Britain ceasing the blockade of Germany. Of course, the war is not a conflict between London and Berlin alone, but they were most influential members of their respective sides.
Another idea (which I might turn into a TL at some point, real life permitting), has Tsar Nicholas and General Brusilov killed in an Austro-Hungarian bombing run in April 1916. The main Russian summer offensive is directed against the Germans and ends in failure. With more reserves, the Germans capture Fort Souville, and French casualties mount ever higher. The Germans have more reserves for the Somme, so they come out a bit better. In Italy, the Strafexpedition still peters out, but without Brusilov the KuK army has the reserves to blunt the Isonzo offensive later in the year. You might add a worse Jutland to get the British more on edge, or have Lloyd George be drowned with Kitchener.
The above scenario, where things are more inconclusive than OTL, is somewhat more conducive to getting everyone looking at other options. However, I won't say I'm wholly convinced, and no doubt many others will feel even less confident.