Sky Sports revealed West Ham's interest in the £8million-rated striker earlier this summer.
The Hammers applied for a work permit for the 22-year-old and were hopeful that they would win a deal for Zapata, who is expected to be part of Colombia's squad for next year's World Cup finals.
But now Sky Sports understands that West Ham have decided to pull back from the deal and are looking at other striking targets.
Zapata, who is believed to have other interest in England, has also attracted interest from Italy and Spain with the likes of Sassuolo and Atletico Madrid both said to be keen.
The player himself has insisted he is in no hurry to leave, telling Ole: "If I do leave then the board need to find a new striker, a target man, so my idea is to stay."