It is generally believed by scholars that Christopher Columbus, before setting out to find his new route to the east that landed him in North America, petitioned Paolo dal Pozzo Toscanelli (1397 - 1482) for advice. Toscanelli was a famed astronomer, cosmographer, and mathematician who studied at the University of Padua. In fact, Toscanelli became the world's most distinguished scholar in cosmography, the science of the mapping of the universe, in the 15th century due to his expertise in Ptolemy, his devoted studies of Marco Polo's travels, and knowledge he gained from merchants, especially the famous Venetian merchant Niccolo de Conti (Catholic Encyclopedia, "Paolo dal Pozzo Toscanelli"). Hence, due to Toscanelli's extensive knowledge of cosmography, it is widely believed that Columbus asked Toscannelli for advice about the voyage. We also know that Toscanelli very strongly believed that a western route to Asia did exist.
However, it seems that Columbus did not write to Toscanelli himself. Instead, King Alfonso repeatedly wrote to Toscanelli for advice about the prospective voyage, and Toscanelli finally responded by writing the famous letter to Canon Ferdam Martins of Lisbon on June 25, 1474. Some scholars believe Toscanelli also sent a copy of the letter to Columbus. The letter contained a map giving a clear, suggested route.
However, while a copy of the letter has survived, other scholars believe there is no clear evidence that Columbus and Toscanelli communicated directly since the letter is addressed to Canon Ferdam Martins of Lisbon. In addition, as the editors of the Complete Dictionary of Scientific Biography inform us, Columbus sailed a different route than Toscanelli indicated on the map:
Moreover, Toscanelli favored a route on the Lisbon [Portugal] parallel, whereas Columbus held to that of the Canaries, fourteen degrees farther south; and when he reached Hispaniola he was convinced, after having traveled sixty degrees west, that he had arrived at Cipango (Japan). According to Toscanelli's map, he would have been forty degrees away. ("Columbus, Christopher")
Hence, while it may be clear Columbus had been inspired by Toscanelli's ideas, it looks like there is not enough evidence to support the idea that he and Toscanelli had been in direct communication via letter to discuss routes.