Allardyce was addressing reporters ahead of his side's trip to the Emirates Stadium.
He has, however, highlighted a few worries as well, revealing that Enner Valencia and Alex Song are both suffering with injury problems, while defender Carl Jenkinson is ineligible to play against his parent club.
He told reporters at his pre-match press conference: "Enner has had an accident at home and has cut his big toe quite severely on a broken cup. It has been stitched.
"We're not sure if he will be considered for this game. It was a freak accident."
Valencia has been problematic for opposition defences this season with his pace and pressing, so to lose him before a trip to one of the contenders for the top four is a big blow for the side, as would the potential loss of former Arsenal man Alex Song.
The West Ham boss added: "Alex has a bit of a knee problem. It's better he stayed here for treatment."
The Hammers are on a pretty poor run of form at the moment, having not won in each of their last six Premier League games, which is putting a dampener on what was a very promising start to the season. As a result, they have slipped down to 10th place in the Premier League.
There is an acknowledgement from Allardyce that Arsenal have improved this season which sees them currently lie in third place, though they still have much work to do if they are to finish in the Champions League places yet again.
Big Sam has highlighted areas where his side needs to be at the top of their game, saying: "We've gone to Arsenal a couple of times and got in front, but unfortunately the leads haven't lasted very long!
"Facing Arsenal is more difficult at their own place. On the day at our ground there was not much between the two teams.
"They have adapted to change the way they play to win football matches. We must take our chances and defend strongly.
"They have a few weaknesses but if we can expose them and take our chances is down to how well we perform on the day."