Maybe he studies old scripts, which describes the sagas of the old Norse (they existed) and has the idea to find this mysterious Greenland. He probably thinks, it is a rich lost colony. Maybe he can go to the King of Denmark and ask for aid. Than he miraculously finds Greenland and make contact to the last remaining Viking colonistst who haven´t seen a ship for a long time.
The Greenland colonists would already extinct at this point - the colony failed earlier in the 15th century.
But with the demise of the colony only a short time in the past, and the buildings undisturbed, Columbus would certainly have been able to locate the remains of the colony if he knew where to look.
There is one more factor would be in Columbus´ favor if he took the Northern route. IIRC his big problem when finding a backer was that he proposed to sail out into the open ocean, when nobody knew for sure how long it would take to reach his destination, i.e. if the ships would actually be able to make the voyage with the provisions he carried.
With the Iceland-Greenland-Vinland route, on the other hand, it was pretty well known how long the voyage took, and even the Norse of 1000 AD with their far less sophisticated navigational methods (and probably less seaworthy ships) made the voyage repeatedly - so hardly anybody would have doubted Columbus´ ability to reach Vinland.
And, operating from a base in Vinland, going further west to China would be a far less ambitious undertaking, even discounting the possibility (as his contemporaries might have believed) that Vinland was the northeastern end of the Asian continent and Columbus would simply have to follow the coast southwest to get to China.