When the "New World" was discovered the African slave trade was already well underway in European countries, as well as in Africa itself. American Indians were never exactly chosen for slavery, but the idea was not completely missing. In Christopher Columbus' journal he remarked upon his arrival to the Caribbean that the men and women there were savages and could be easily dominated.
However the relationship in the regions were often used as more of a friendly neighbor type system. The Europeans (except the Spanish) did not come as conquerors but more as settlers and thus were not primed to dominate a foreign people in a foreign land they did not already have control over. This meant that it was more beneficial to trade with and work with the Native Americans rather than attempt to subjugate them.
Once the settlers grew in power and force, they used their ability to move their 'allies' out of previously owned lands and into territories that were not in use. This led to events such as the Trail of Tears under President Andrew Jackson. African slaves were never used primarily for trade because the thought of working alongside them was foreign, and the peoples of Africa had been subjugated long before the first Europeans began colonizing North America.
In South America the Spanish were planting their roots in the late 1400's. Slavery was already on the way out by this point and Spain completely eradicated slavery in 1542. Slavery was not their style, instead they completely dominated the Incan people they found on their conquests.