Wickham was playing for Sunderland when the Hammers registered an interest in his services, and the move was very close to going through.
The 22-year-old forward says that West Ham were keen on signing him, but last minute issues caused the transfer to be blocked.
"I got close to joining Sam at West Ham but it fell apart at the last minute," he said.
"It didn't go to plan at Sunderland. The idea was that I would be the focal point of the team and it didn't work out that way.
If Wickham had moved to West Ham he would have added even greater cutting edge to a forward line which is already packed with talent.
The Hammers have assembled a talented group of attackers, but Wickham would have given them even more quality.
Palace have benefitted from the England youth international’s failure to complete a move to Upton Park, as they moved to snap the forward up this summer.
Wickham’s progress at Palace has been halted due to injury so far, but he is returning to full fitness now, and will hope to make an impact as the season progresses.