Well, peoples in North Germany retained relatively close ties (intermarriage of the ruling class, common cultural elements etc.) with Scandinavia until Charlemagne came along and defeated the Saxons. Earlier Christianisation of more southern areas in Germany (for instance, the Frankish lands) had in fact driven the Saxons to orient themselves towards Denmark etc. The last Saxon duke, who led the Saxons in their war against Charlemagne, was a friend of the Danish king (and I think married into his house), and fled to Denmark twice during the conflict.
If Charlemagne dies during the Saxon Wars, and the Franks fail to conquer the Saxon lands, you'd end up with a northern area that continues to resist conversion (for the moment) and is clearly separate from the Christianised areas further south. This doesn't exactly imply Scandinavian settlement in northern Germany, but if these lands continue to be closely allied (driven into each other's arms by the threat from the south), I can easily see a Canute-like figure turning it into a single northern realm during or after a major struggle against the Franks (or their successors in the role of Christianising force).
That way, you'd end up with a northern Germany that's culturally Scandinavian, more or less.