EDIT: ok, if the Allies knew of the massacres and genocide, why didn't they threaten the German soldiers and citizens with genocide if they didn't immediately stop?
Via leaflet, radio and television: 'To the people of Germany. We have learned and verified via our spies that German military forces are murdering millions of Jews, Gypsies, and political enemies in death camps. You must cease this genocide immediately!
If you do not comply we, the Allies, will show no mercy to German soldiers, and when we eventually conquer Germany, all German citizens will be annihilated. Every man, woman, and child of Germany will be executed by firing squad, and your land will be given to your neighboring countries.
You must stop your murder camps, or all of you risk extinction. '
The information was widely available in 1942, years before D-Day.
There were rumors from very early on. The Germans had established the first concentration camps in the '30s to deal with communists, socialists, and other enemies of the state. These were different from the mass extermination camps that would be seen later on. So when reports started coming in about killings in camps, it was of course seen as terrible, but nothing extraordinary. Additionally, it wasn't just the Jews being slaughtered, so there wasn't a clear picture of what exactly was going on.
In 1942 as the killings increased, more information began leaking to the public, thanks in large part to some pretty heroic work by the Polish resistance. Here are some quotes from newspapers at the time:
London, July 1 - The Polish Government in London has been urged in a report on the slaughter of 700,000 Jews in German-occupied territories to call on the Allied governments to adopt a policy of retaliation that will force the Germans to cease their killings.
New York Times. July 2, 1942.
London, July 26 - The German murder toll in Poland is reaching a new high with the total victims estimated at 3,200,000, including 1,800,000 Jews, as of May 1, it was asserted today by Wladyslaw Banaczyk, Polish Minister of Home Affairs.
New York Times. July 27, 1943.
London, Feb. 16 (U.P.) - The Polish Government in Exile charged today that "Germany's diabolical attempt to exterminate the Polish nation" had resulted in the death of "scores of thousands" of Polish children and the complete extermination of all Jewish children in Poland.
New York Times. February 17, 1944.
Eventually the Polish underground conducted extensive surveillance and got the information to the Alllies on the extent of the Holocaust once it had picked up steam. Here is an example of a report given to representatives of the Allies from the surveillance. On December 17, 1942, the Allies made this public statement:
The attention of the Belgian, Czechoslovak, Greek, Jugoslav, Luxembourg, Netherlands, Norwegian, Polish, Soviet, United Kingdom and United States Governments and also of the French National Committee has been drawn to numerous reports from Europe that the German authorities, not content with denying to persons of Jewish race in all the territories over which their barbarous rule has been extended, the most elementary human rights, are now carrying into effect Hitler's oft-repeated intention to exterminate the Jewish people in Europe.
From all the occupied countries Jews are being transported in conditions of appalling horror and brutality to Eastern Europe. In Poland, which has been made the principal Nazi slaughterhouse, the ghettos established by the German invader are being systematically emptied of all Jews except a few highly skilled workers required for war industries. None of those taken away are ever heard of again. The able-bodied are slowly worked to death in labor camps. The infirm are left to die of exposure and starvation or are deliberately massacred in mass executions. The number of victims of these bloody cruelties is reckoned in many hundreds of thousands of entirely innocent men, women and children.
The above-mentioned governments and the French National Committee condemn in the strongest possible terms this bestial policy of cold-blooded extermination. They declare that such events can only strengthen the resolve of all freedom-loving peoples to overthrow the barbarous Hitlerite tyranny. They reaffirm their solemn resolution to insure that those responsible for these crimes shall not escape retribution, and to press on with the necessary practical measures to this end.
So we can safely say that the world knew what was happening by the end of 1942. However, knowing/reading about something on the other side of the world is far different from being at the camps and seeing the people, or even seeing the pictures that came out after the fact. So while people knew that it was happening, the true horror wasn't really internalized for most people until after the liberation of the camps.