Did anyone in Europe predict the existence of the Americas?

This is far from proven science, maybe not even at the level of a hypothesis. Supposedly the king of Mali in Africa sailed to the Americas around 1300 or earlier. Don't remember the exact years. Some people have also suggested that some of the statues found in central and south america look African and this could indicate a voyage from the old world that we don't know about.

I also like to read Graham Hanc**k once in a while and in one of his books he said that supposedly Columbus spent a long time on some island that had a tradition of sailing and navigation going back thousands of years and they had secret maps that depicted the Americas.

King of Mali

There is some evidence to this, but not proven. I've seen the statues on TV and they do look African. Also some of the artwork from ancient mesoamerica seems to be based on the same constellations as that from the Middle East and Asia. Some of this will take time. I don't follow Hanc**k religiously, but some of the things he talked about in his 1993 book are coming to light.

Fingerprints of the Gods was written before Gobelki Tepi had been studied in detail.

Magicians of the Gods No, I don't believe there were 7 magical people who fled Atlantis or whatever and sailed the world. What I do think after reading this is that there is something beyond mere coincidence to explain why artwork is based on the same constellations around the world. And that people may have studied the stars and mathematics earlier than we currently know.

None of this stuff is close to being any kind of proof, but you have to wonder sometimes. Sailing then wasn't like it is today. It was extremely dangerous and doing so into the unknown even more so. It was also insanely expensive and why would a new king give Columbus so much money on such a risky venture?

When I was in school we were taught Columbus discovered America. Today we know it's not entirely true. In 50 years we might find enough evidence that people have sailed across the oceans for thousands of years.

Europeans, perhaps not, someone in the old world, yes.

Al-Biruni (973–1050) lived in Khwarezm (modern Uzbekistan). Among other works in mathematics, astronomy, physics, mineralogy, history and geography, he calculated the circumference of Earth with a precision higher than his predecessors, and made some precise maps of known lands. In his work Codex Masudicus he conjectured that there should be an inhabited continent between Europe and Asia:

But was three fifths of the Earth’s circumference really nothing but water? Biruni considered this possibility but rejected it on the grounds of both observation and logic. From his study of specific gravity he knew that most solid minerals were heavier than water. Would so watery a world not give rise to serious imbalances to which the planet would have had to adjust over time? And why, he asked, would the forces that had given rise to land on two fifths of the earth’s belt not also have had an effect on the other three fifths as well? Biruni concluded that somewhere in the vast expanses of ocean between Europe and Asia there must be one or more unknown land masses or continents.

(Source: S. Frederick Starr)

His reasoning was unsound from the modern point of view, since the same arguments would imply, for example, that Pangea could not exists. But the conclusion was correct.

There is no evidence that this work was known to Columbus, but, interestingly enough, he did know a work of central Asian geographer Ahmad al-Farghani (c. 800–c. 870) who computed the circumference of Earth more accurately than the Greeks (but less accurately than al-Biruni). There is a theory that it is a confusion about the units used by al-Farghani that led Columbus to underestimating the circumference of the Earth, underlying the whole rationale for his trip.