The early Luftwaffe under its chief of staff, Walther Wever, toyed around with the concept of the Uralbomber, large four-engined bombers that would conduct strategic bombing of the Soviet Union. There were some resulting designs, such the Ju-89 and Do-19, but the Germans soon abandoned these efforts. Wever's death in 1936 eliminated a prominent advocate for strategic bombing, but also the limitations of German aviation industry arguably played a larger role than Wever's death. German industry could not produce large numbers of four-engined aircraft, especially engines which were an enormous bottleneck for German industry. German bomber doctrine after Wever increasingly embraced the Schnellbomber concept of fast medium bombers that could quickly reach their targets before any interception. Producing these advanced medium bombers was well within the means of German industry and the Luftwaffe entered the Second World War with a large force of medium bombers. Although wartime experience proved many of the concepts behind the Schnellbomber false, it became one of the principles for German approach to designing bombers during the war. The He-177 was the baleful culmination of this process in which a large strategic bomber had to maintain the speed of the Schnellbomber and perform similiar tactical missions like dive-bombing. The result was a technical monstrosity that performed neither of its tasks very well. The US entry into the war meant that Luftwaffe planners had to think in a more expansive goegraphic scale which prompted the Luftwaffe to rethink the Uralbomber concept and resulted in the so-called Amerika-Bomber design competition. These were large four-engined bombers with enough range to theoretically fly to New York from advanced bases in Europe. The most famous Amerika-Bomber design was the Me-264. Yet the Amerika-Bomber could not escape many of the problems that hamstrung its predecessor as German industry had difficulty in producing large, technically sophisticated aircraft. The war exacerbated many of these difficulties, creating enormous shortages of high quality materials. The Amerika-Bomber prototypes were largely disappointing aircraft and the program turned out to be a diversion of German resources.
Sources
Corum, James S. The Luftwaffe: Creating the Operational Air War, 1918-1940. Lawrence: University Press of Kansas, 1997.
Murray, Williamson. Strategy for Defeat The Luftwaffe, 1933-1945. Maxwell Air Force Base, Ala: Air University Press, 1983.
To add on to /u/kieslowskifan's good answer, here is an answer I gave to a similar question a while ago.