The Wales midfielder is recovering from a knee injury.
West Ham cruised past Burnley in the FA Cup last-16 on Monday and are now just one win away at Stoke from a Semi-Final appearance at Wembley.
Collison said: "The boys were unlucky in the Carling Cup so it would be nice to have a run in the FA Cup - by getting through the next couple of rounds so we give the fans a day out at Wembley.
"I would definitely hope to be fit for the Final. It's a big time to be at the football club and I can't wait to be back playing."