1916 was as good a time as any I think-
It's not probable, but I'd call it plausible.
So I guess I'm diasagreeing with Kalvan here.
Why? Because in 1916 and early 1917 neither side was reeling, and both sides had assets that belonged to the other that could be traded for a status quo ante peace. In 1914 and 1915 (least until autumn), both sides, especially the Germans, could still hope for a knock-out blow. Later in the war Germany did get a knock-out blow versus Russia, but then the Allies saw the effects of the blockade and the Americans coming in behind them if all else failed.
But in the period from very late 1915 through the first half of 1917 the sides were more evenly balanced. In 1916 in particular:
Germany had Belgium, occupied France, Poland, Serbia.
The Allies had German colonies in the Pacific, and Southwest Africa, Togo, and were wrapping up Kamerun and had occupied big chunks of German Est Afrika though Lettow-Vorbeck still had a force there.
It would have taken some convincing on both sides definitely. I agree with Grimm that the principal obstacle was the German leadership. I also agree with Imajin that pursuit of the Austrian initiative might be the best hope.
The PoD would be a different set of German calculations - They could look at the situation in 1916 and see that:
1. The diplomatic hand Germany had been dealt really sucked, it was facing a huge coalition of its largest and most powerful neighbors, but was allied "to a corpse" in Austria, and to habitual losers of wars Turkey and Bulgaria. Ideally, a reshuffling of the diplomatic deck should be achieved by knocking out one opponent and making a separate peace. But, considering the lack of German reserves for offensives, that wasn't regarded as practical. So, the only hope for a diplomatic reshuffling, breaking up the Entente, could be peace. After a status quo peace the Entente might try to hold together, but Germany could try to see about working with Britain (desirable but still unlikely) or Russia, and dropping its weaker allies.
2. The situation in the Atlantic was only making it worse. In early 1916 the Germans had to back down on using unrestricted U-Boat warfare in the face of an American ultimatum and inadequate capabilities. So at this point they knew they could either have U-boat warfare and the Americans against them, or they could keep the Americans out by sacrificing U-Boats. If they went for a status quo peace [I will free Belgium, but only if I can send landing parties back to my African colonies, etc.] they could neutralize the American drift toward the Entente. They could improve relations with the US by appealing to Wilson's vanity in brokering a "Peace without Victory".
3. They had finally beaten the country they could scapegoat for starting the war, Serbia. The Central Powers could propose a status quo ante bellum peace, with the exception that Serbia pays an in-kind indemnity and it loses some territory to its neighbors (Sanjak to Austria, Kosovo to Albania, Macedonia to Bulgaria). That leaves the war a technical Central Powers win.
If, by accepting this, the British can get Belgium freed, they might consider it worth it. Russia would have a stake in opposing the reduction of Serbia, but in 1916, they could get the restoration of their Polish territories, a relief from a straining war, and could claim a partial restoration of what had been a completely occupied Serbia. Meanwhile Germany has demonstrated its credibility as an ally, and can advertise that when it tries to acquire new allies.
Of the Allies, only France itself at this stage will declare Alsace-Lorraine the make-or-break issue. But France needs its allies to win them, and if those allies are ready to make the deal described above, they might not tolerate French obstruction.
If the Allies make a full territorial restoration of Serbia a condition for accepting the overall peace, Germany can probably pressure Austria to swallow it, considering Austrian peace efforts at the time. Instead of losing territory, the Central Powers can claim the ravaging of the Serbian countryside, the seizure of Serbian movable property, the execution of Serbian war criminals, and maybe the deportation of Bosnian Serb nationalists (or maybe all Bosnian Serbs?) to Serbia has "taught the Serbs a lesson" even if they get territory restored.
4. Austria, the ostensible partner who brought Germany into war, was starting to go soft. If they, who dragged us into the struggle, now want to quit, what can you do?
Anticipating counter-arguments-
Objection #1. When the Allies see that the Germans are willing to accept less, they will think "yippee, the Germans are weaking". With Allied morale improved they will press the attack and the Germans, less certain about the war, will start to fall back and then crumble.
Rebuttal to # 1. The Germans still have robust and strong lines. The Germans can sustain their own morale by casting the war in defensive terms, ie "the Allies are proving they want to pick us apart and rearrange us like Napoleon- now this, allow we cannot". German lines held until remarkably late in 1918, in the alt-1916, there has been two years less degradation.
As far as the Allies are concerned, they might get giddy in anticipation of German surrender, but that morale boost might only last 6 to 8 weeks. Costly battles like the Somme and Brusilov offensive will demonstrate that Germany is not yet ready to cave, and will make the status qo peace option look more attractive on the allied side of the line. Meanwhile, Woodrow Wilson will move further away from the Entente diplomatically, as Germany is more in line with the "Peace without Victory" concept, and the memory of the Irish Easter Rising is still fresh.
Objection # 2. There will be a revolution in Germany if it proposes to settle for less.
Rebuttal to # 2. This one is more serious. There will certainly be shifts in power domestically, and pressures for reform. Liberals and socialists will benefit. However, Germany has still suffered two less years of damage, and the aristocrats and bourgeois still have their interests to defend even if the military policy looks like a failure. To sustain the morale and viability of right-wing forces in Germany, the establishment can try scapegoating socialists and/or Jews for weakening the war effort. They can also publicize Austrian attempts to cut a deal. So there are many candidates for a stab in the back, who can be blamed for not achieving a full victory. Meanwhile, Germany can try to cast itself as winning a defensive war against allied powers who had an agenda to partition Germany. Germany could try to use this as its War of 1812, where the US gained nothing but still felt like a winner. The German Empire would be about as old at this point as the US was in 1812, a young state in its 40s.
Objection #3. It will be hard to get distant allies like Japan, Australia, New Zealand and South Africa to disgorge their gains from German colonies.
I basically agree. Japan has no motive to trade back Pacific territories for changes in Europe.
But these final differences could probably be finessed by having the countries that have these territories pay a nominal fee for them, stretched out over long-term small, installments.