The Hammers provided one of the biggest shocks of the season in their most recent outing, beating high-flying Tottenham 3-0 at White Hart Lane.
Two weeks after that fine victory, Allardyce is keen to secure another big-name scalp and possibly move into the top 10 in the Premier League.
"We're looking forward to the Man City game now. They've faltered a little bit away from home and hopefully we can capitalise on that," Allardyce said.
"They've also had a lot of players on international duty and we've got to think about that. We want to upset the odds on Saturday.
"Last time we had an international break we lost the game before. This time we won and it makes everyone's life a bit easier.
"In terms of results they've been a bit Jekyll and Hyde. We have to be encouraged by their away results. Last year we drew 0-0 here against them and we have to hit top form with our top players as we did at Tottenham again.
"Nobody gave us a chance at Spurs, but we won 3-0 and that's why the entertainment value in the Premier League is so high. It's hard to predict what's going to happen."
Allardyce is likely to be without James Collins against City after the defender injured his hamstring playing for Wales.
You can catch West Ham's clash with Manchester City live on Sky Sports 1 on Saturday evening, with the programme starting at 17:00