The Hammers have a quarter-final replay with Manchester United ahead on Wednesday.
The Irons are currently sixth in the top flight - five points adrift of Manchester City in fourth - and have a quarter-final replay with Manchester United to look forward to on Wednesday.
But when asked whether he would deem one competition more important than the other, the Croatian's answer was emphatic.
"The FA Cup always. It's obvious. I can't imagine any manager saying opposite, that he would rather take fourth in the league, when you still have to qualify, than the FA Cup," he told the Star.
"The FA Cup is a trophy. It's a historical one."
With success on either front having major positives, it is perhaps a surprise that Bilic has come to the conclusion that winning the FA Cup would be a greater achievement than finishing fourth.
While the Hammers would not get a trophy for a top four spot, finishing that high would give them an excellent chance of progressing into next year's Champions League.
However, with a five point gap to claw back with just six games to go, Bilic's assessment could well be slightly tactical as he may feel that winning the FA Cup is more likely and thus, giving it extra importance would make it a greater achievement if they manage it.
If Bilic's men can see off Louis van Gaal's side on Wednesday, then they would be the last top half team left in the competition so would surely go into the semi-final as favourites.
In the league however, they are underdogs to take fourth so Bilic may have decided to target the more probable achievement to ensure that they stand a better chance of ending the campaign on a high.