At the very least he would have known about the existence of a landmass.

As many know, Columbus landed in the Antilles, believing it to be Asia. The crucial fact that this was a new landmass was not widely accepted until Amerigo Vespucci was appointed the piloto mayor or "Navigation Chief" of Spain in 1508 and presented his idea that the Antilles and other islands were not an eastern edge of Asia, but rather an entirely new as yet undiscovered landmass. Vespucci even coined the term"new world" in an earlier letter written by him to Lorenzo di Pier Francesco de' Medici in 1503. Medici died shortly thereafter.

Now, I am not an expert on Da Vinci himself, but I can recall that the Medici family were prominent patrons of Da Vinci. Lorenzo the Magnificent was certainly a patron of Da Vinci. Amerigo himself was was employed by the Medici.

Therefore, even if nothing exists in Da Vinci's writings about the new world (I'm not sure if it does or not) we can be reasonably sure that the news of the discovery and acceptance of a new landmass had made its way to the top echelons of Italian society by 1503. Therefore, Da Vinci assuredly would have known of its existence before 1519 (by which time the Spanish had already reached the Pacific Ocean in 1513 - Vasco Nunez de Balboa having crossed the isthmus of Panama).

As /u/ColossalMistake has already discussed whether Leonardo Da Vinci would have known that Columbus' "discoveries" made up a "New World", I'll look some more at the circulation of Columbus' writings themselves. I'd especially add that information did not travel as slowly at the turn of the 15th c. as one might imagine - especially for members of the elite (like Leonardo, although I can't speak on mentions of the Americas in his works either).

Columbus' letter on his first voyage from 1492 was transcribed and circulated in 1493, with a Latin translation following shortly after. This copy was then translated into Italian in Rome still in 1493 (as the Epistola) and became a publishing success. Cecil Clough argues that no exact estimates of publication numbers can be given and goes on to detail later translations of this letter (p. 299):

On the basis of the first Rome printing, there followed, apparently within a few month, three printings at Paris, one at Antwerp, and illustrated one at Basel, all in Latin. There were at least seventeen printings of the Columbus letter in the fifteenth century, including a translation into German in 1497. A free translation into Tuscan verse was printed during 1493 and over the following two years was reprinted at least four times. In sum, between early 1493 and 1500 some 3.000 copies of the letter were published, at least half of these printed on the Italian peninsula, and since more than half of the copies were in Latin one can assume that humanists were well represented among the readers.

Clough also mentions that Vespucci's later writings proved even more popular than those of Columbus; and crucially that the major number of printings on the Americas at the time circulated from Italy to the continent. This was greatly aided by the quite recent spread of the printing press (in use from the 1460's onwards in Italy). Regarding your question I'd like to highlight first the importance of Italian translations and printings of both Columbus' fist letter and Vespucci's writings in spreading news of the Americas - that were not identified as new lands by Columbus himself. And second the large number of Latin copies printed in Italy suggesting many humanist readers of these writings. Taken together, both make it seem very probable to me that the Italian humanist Leonardo had had in some way made contact with Columbus (and later Vespucci's) works in the early 16th c.

Just to give a short example just outside of your time-period of how relatively fast important news could travel at the time in elite circles: Benjamin Keen argues that writings on Cortés' campaigns against the Aztecs in Mexico until 1521 had been circulated widely in the 1520's, both from Cortés' letters and from Peter Martyr's Decadas, so that "[b]y the third decade of the sixteenth century Aztec civilization had entered the consciousness of many cultivated Europeans if not of the masses." - this only roughly 10 years after Cortés' landing in Mexico.

Sources:

• Cecil H. Clough: The New World and the Italian Renaissance, in: The European Outthrust and Encounter: The First Phase C.1400-c.1700, ed. by ibid.

• Benjamin Keen: The Aztec Image in Western Thought.