In April 1912, when the Titanic sank, the best of the pre-WWI German U-boats were the U-13 type. They had a maximum operating range of about 4,000 miles. Although the first three U-13 type boats had been launched, the first two, U-14 and U-13, were not commissioned until April 24th and 25th, 1913 (respectively). Since their commissioning ceremonies were well attended, they could not have deployed to the north Atlanctic and returned in time.
That means that the U-9 type boats (U-9 through U-12) would have been the best available. The problem is, these small boats (170 feet in length and 23 feet high when surfaced) only had a 3,300 mile maximum operating radius.
The distance from Germany to Newfoundland, via the English Channel is about 3,000 miles. This means, unless the U-boat was on a one-way mission, or was otherwise logistically supported, no German U-boats of that vintage could have possibly carried out the mission. Furthermore, because of the U-boats low top surface speed (8 knots), and even lower submerged speed (1-2 knots), it would have nearly impossible for the submarine to know where the very fast Titanic would have been at any time in its voyage.
Since the German report no U-boats lost at that time, the one way mission is not plausible. I suppose the author of the article could imagine a secret German Arctic submarine base, or claim they had developed at sea refueling from a German tanker assigned to accompany the mission. These are just as plausible as the orignal post.