The Hammers are in FA Cup action this evening when they take on Everton in a third-round replay at the Boleyn Ground.
"A cup run would mean a lot to the club,” the 27-year-old told West Ham’s official website. “Everyone wants to play in the FA Cup, it's such a big trophy with so much history and it gives the fans a massive buzz if you get to the latter stages.
"It becomes a right good feeling around the camp to get to those games. It would be disrespectful to Everton to start talking about that yet, because we have a big game against them and we need to win that first.”
West Ham have a very good and strong squad this season, and the fans have every reason to believe that they can go far in the FA Cup.
Although things have slowed down a bit for the Hammers in recent weeks with results not as good as expected, the London outfit are very much in the running for a top-four finish in the Premier League.
Many would see the FA Cup as a distraction to West Ham’s top-four ambitions, but a cup run is going to be important for the team’s confidence.
Given the large squad at Allardyce’s disposal, he does have good players to field in FA Cup ties.
Of course, talks of winning the FA Cup at this stage of the competition are premature, but West Ham should give it a go.