Yes and no.

Did the Germans know that at some point the western allies were preparing to open up another front with landings in mainland europe? Yes, that would have been difficult to hide considering the amount of preparation that went into that kind of thing and it was clear that Italy wasn't a road to Berlin. The Germans had long known of the possibility of an invasion somewhere and so had been building up the length of the Atlantic Wall over the last two years to attempt to defend from such an invasion.

However they didn't exactly when or where it was coming. Specifically as to the were the allies did a lot of work to feed false information to the Germans as to the where part as part of operation body guard. Via a number of methods western allied forces aimed to convince that the primary landing areas would be Calais with a smaller one in northern Norway and and additional attacks would be feints. This was via a number of methods, firstly the double cross system. MI5 had a number of double agents who fed the Germans false information supposedly gained from fictional networks of secrete agents in Britain who were actually working for or with British Intelligence Services, these were used to suggest that these alternative landing areas were the primary targets while concerning the date of the invasion aimed to try make it as ambiguous as possible while appearing to be good intelligence sources.

Additionally there was physical deception via the ghost army, dummy airfields and troops positions along the British coast in places where German aircraft might spot them that would be convincing enough from the air to suggest landing operation further east than the allies planned to do. This type of thing was complimented by producing things like radio activity to build up the impression of the existence of such a force.

Additionally via operation Graffham and Royal Flush the diplomatic services of Britain and the US began to communicate with neutral embassies in Sweden, Spain and Turkey, Sweden in particular the negotiations were supposed to suggest that the allies wanted to ally with Sweden for liberating Norway and negotiations with all three countries were supposed to suggest these fake invasion plans. The idea being that one of the three neutral governments might either hand the information along to the Germans or potentially there my be German spies or sympathisers within the neutral country's diplomatic services and embassy staff who might pass the false information along.

As for the exact day the Germans didn't know when D-Day was coming. By summer 1944 it was clear it was coming sometime soon but the Germans couldn't know exactly when, specifically in the recent days before June the 6th the poor weather made the Germans relax a little, landing large numbers of troops on beaches and paradrops would have been difficult in stormy weather and the Germans thought this weather was likely to continue for the next few days at least. The allies who had radar equipment and ships out in the atlantic sea though could see that while the weather wasn't going to be perfect for an invasion that there was going to be a large enough gap in the windy, wet weather coming from out at sea that would let them do for it. Of course this had its upsides and down sides, while the Germans were more relaxed it also made things harder for example for the goal the allies had of trying to rush off the beaches and seize a number of D-Day objectives like Caen and Bayeux for the first day of the invasion and between this and Omaha not going as well as planned allied forces didn't manage to move as quickly as they hoped with particularly Caen turning into a hard fight with the Germans over the town and the surrounding area.

But on the day a lot of German forces were elsewhere along the coast, notable German officers like Rommel were on leave and many like Falley had been away from the front wargaming (and he specifically was killed by paratroopers while trying to make it back to his men in time). Even after D-Day began the counter intelligence had worked so well that initially until the scale of the Normandy invasions got back to German command they still weren't entirely convinced Normandy wasn't still a decoy for another invasion and some troops remained in Calais for a while.