It's not likely at all -- in fact, "likely" isn't the right word to use, because they did not. This section of our FAQ goes into various theories of pre-Columbian contact, and though it does not mention the Phoenicians specifically, they did not voyage to the Americas.

Based on our current knowledge, there were three times the Americas were "discovered" by groups of people:

1. Groups living in Asia expanded eastward and then southward into the Americas starting between 15,500 and 13,500 years or so ago, possibly exploiting lower sea levels to cross what's now the Bering Strait on land, or possibly using small boats or other vessels to sail along the coast, or possibly a combination of the two. Those peoples became the various groups of indigenous Americans that peopled the Americas before Columbus and still exist today. (There was also trade and contact between Asia and the Americas after sea level rise cut off the Bering land bridge, but that's a separate question.)

2. Norse explorers settled in what's now called Greenland starting around the 980s or so, and the colonies there lasted until the 1430s. The Norse also established a short-lived settlement in what's now Newfoundland, at L'Anse aux Meadows, around the year 1000.

3. Columbus and his crews voyaged from Europe in 1492, landing in the Caribbean and, in further voyages, spurred the age of exploration, colonialism and genocide in the Americas known as the Columbian Exchange.