The 22-year-old striker is currently with Argentine giants Estudiantes and a host of clubs have been tracking the £10million-rated marksman.
Borussia Dortmund, Lyon, Besiktas and Benfica have all shown an interest in the Colombian, who scored 14 goals last season in the Argentine top flight.
However, West Ham - who have strong links in South America - have been keeping tabs on Zapata for a number of months and they have now decided to make a move for the powerful 6ft 2in front-man.
Zapata is yet to make his full debut for Colombia, but it is believed he will be part of their squad before next summer's World Cup finals, which they are on course to qualify for.
Zapata is being tipped to become the next Colombian to break into European football following on from the likes of Radamel Falcao and James Rodriguez, who began on the same career path from their homeland, to Argentina and then Europe.