The Hammers will move back into fourth place, above Arsenal, if they take at least a point against Norwich on Wednesday.
Norwich remain at the foot of the table, but Moyes is not taking them lightly, although he has his sights firmly set on a third straight win and another three points towards their bid to gatecrash the Champions League spots.
“Norwich have got a really good manager in Dean Smith. It’ll take a little bit of time to get things sorted,” he said.
“They’re in a fight to stay up, but I think there’s a chance for the bottom five teams – there’s a fight on.
“Norwich will see every game as an opportunity, but I see it at West Ham as a chance to challenge the teams at the top and keep annoying them.
“I was really pleased with the two wins, and the FA Cup win against Leeds United because it’s like three Premier League wins in a row.
“We’ll treat our next game against Norwich in the same way we’ve treated the other ones.”
West Ham have been hit by injuries to defenders Aaron Cresswell, Angelo Ogbonna and Kurt Zouma, forcing Moyes to look for cover this month.
Zouma could be back from a hamstring injury sooner than expected, however.
“Kurt’s doing well. I couldn’t give you an idea of exactly when he’ll be back. We’re just trying to get him correct and in the right condition as well. Hopefully he’s not too far away,” added Moyes.
“We could probably do with some more cover because of Angelo Ogbonna’s season-long injury. If I can get Kurt back that eases the pressure, but we’re always looking to strengthen and find players who can help us.
“We’d like to add to our squad if we can and, if we can find players who we think are suitable, we could do with some back-up if we can get it.
“There’s never any guarantee in January that the right players are gettable, but we’re certainly looking around.”