The Irons have a quarter-final replay with Manchester United at Upton Park to look forward to next month as Slaven Bilic's side sit potentially 90 minutes from a date with Everton at Wembley.
West Ham could be forgiven for being disappointed with the replay, given that Dimitri Payet's wonder goal at Old Trafford looked like being enough, before Anthony Martial snatched a late equaliser.
Brooking knows a thing or two about the world's oldest cup competition, having netted the winner when the Hammers last won it 36 years ago, but the 67-year-old believes that long wait will come to an end this season.
“I fancy West Ham for the Cup. You’ve only got to watch them and how they play," he said to The Mirror.
“Slaven wants it and the players want it. He knows how much in our last season at the Boleyn it will mean for our fans if we win it.
“The FA Cup is obviously special for me. It has lost a little bit of its glamour – but not for Slaven.”
By virtue of the fact that Bilic and co are fifth in the Premier League, few would back against them going all the way.
They have been wonderful this season and might yet nick a Champions League qualification spot. The key for Bilic is balancing his priorities and, should he get it right, West Ham have a fine chance at silverware.