This theory is often mention, but historians dealing with Portuguese history usually dismiss it, because first and foremost, there is not a single piece evidence to support this directly, and second it just does not match the behaviour of the Portuguese court and especially the king at the time, Joao II.

Not consistent with action before discovery
You see, Joao II was fully aware that "hiding" any such new land only allows other nation to claim it and he made sure that any new land or island discovered was claimed for Portuguese and was very public about it. He had good reason to, as the Spanish already tried to take over Portuguese operations in Africa during the War of Castillian Succession, but were decisively beaten on sea in a naval battle of the coast of Guinea. As a consequence Joao II was well aware of Spanish ambitions and was serious about making sure that Exploration remains Portuguese only affair.

Now on the other hand there is even an interesting information, that after Columbus approached Portuguese king and was rejected on the basis that his scientific reasoning is unsound (and an additional possible reason that his demand for financing or to be viceroy of the newly discovered region too much for Joao II to stomach), Joao II in 1486 gave permission to his captain Fernao Dulmo to, on his own financing, to go west and search for islands and land, and for it he will be given in similar rights as Columbus was ultimately given by Spain. The expedition was in early stages of planning, set for March 1487, but then nothing more was heard about it, most probably it being abandoned.
This is usually given as a "proof" that at least some Portuguese knew about something being to the west, but it is so speculative (the expedition was planned) and not backed up by any additional evidence, that most probably for people even then it was just a rumour not to be taken seriously. Even if the expedition happened, it would be very, very strange for Portuguese not to claim this land

Not consistent with actions after discovery
Which brings the attention to the second detail why this theory is rejected. After Columbus returned, Joao II was furious. He wanted that land. He claimed it was Portuguese by right. He prepared an armada under Francisco de Almeida to go to America. He also prepared for a land war to fight if needed (or just to show determination), but ultimately settled for diplomatic negotiations under Papacy. In all that time, and in those negotiations, nowhere did the Portuguese made a claim that they already new or discovered those lands. In a matter so important to them you would think they would try if it was true.

Discovery of Brazil
When Portuguese discovered Brazil in 1500, they immediately claimed it and publicized it. Which furthers the point of "hiding" it as something they just wouldn't do. And if they knew from before Columbus, why did they wait almost 10 years to officially discover it?

Why was the treaty of Tordesillas line set where it was
The treaty of Tordesillas happened after the discovery, and has the famous line moved from 100 leagues west of Azores(EDIT or was it Cape Verde?) to 370 leagues, on Portuguese insistence. This line was set by a "commission of representatives of the pilots, astrologers, and mariners of the two nations" to quote Diffie.
The line was chosen for practical reasons. It was given by the Portuguese, on the basis on the wind patterns and currents in the Atlantic so their optimal route between Africa and Azores never crosses Spanish territory. It just happens to be that Brazil is right next to that route, which is how they ultimately discovered it. By accident, while following optimal currents on their trip to India.

Summary:

there is NO concrete evidence of Portuguese discovering America before Columbus, nor any claims by contemporary Portuguese before or after of such a feat, nor does it fit to Portuguese policy (or even common sense) of the time to "hide" such knowledge. There are some actions that could potentially be motivated by Portuguese knowledge of it, but there are other, more plausible explanations for those actions