They did, several times.

1347, a small ship with a load of lumber and a crew of 18 landed in Iceland after being blown off course by a storm. They were Greenlandic Norse who had gone to Markland (America) for lumber for Greenland, as noted in the Icelandic Annals.

It is commonly agreed that the Greenlanders continued to travel to America for lumber and fur, and probably to some extent trade with the natives. The Maine Penny, a Norwegian silver coin from the reign of King Olaf Kyrre (1067-1093) found in Maine might be evidence of trade between the Norse and the natives of America - however, the authencity of the find is heavily debated, with some stating that it is a clear forgery, while others simply say that the evidence in inconclusive.

The end of the Medieval Warm Period and the plague disrupted the ability of the Norse Greenland colony to survive, while inuits spreading southwards started to compete with the Norse over space and fishing and hunting grounds.

The plague killed 50-75% of the Norwegian population and ended all lack of land, as well as the Norwegian ability to have a ruling class that could compete for the throne, which became the prize of fighting Swedish and Danish Kings, with the Danes coming out on top.

Thus, there were no royal power that could fit expeditions and form colonies like the Iberian powers and England did. The abundant supply of land after the plague in Norway meant that there were little to no incentive to emigrate and the failure of the Greenland colony meant that the stepping stone to America was lost.

While the Norse on Greenland did travel to America several times, as their settlement died out and the plague hit Norway, the incentive to go to America was lost, and the Norwegians (and their Icelandic subjects) discountinued their journies.

On a similar token, was it common knowledge in the rest of Europe that there was a permanent European settlement on Greenland, a land mass which we now consider to be part of the North American continent?