The Hammers have made an impressive start to the new season and currently sit fourth, just four points behind the champions going into this weekend's fixture, and Allardyce believes if they can stop most of City's attacking talent, they have a real chance of taking all three points at Upton Park this weekend.
Speaking at his pre-match press conference ahead of the game, the Hammers boss said: "It looks like being the best side since I've been here and the big bonus is the new players hitting the ground running. The rest of the team has been lifted by that increase in quality and energy and we've got over some injury problems too."
West Ham lost on all four occasions they met City last season, with the Champions emphatically beating them in the League Cup in both legs of last season's semi-final, as well as doing the double over them in the Premier League en route to their two pieces of silverware last season.
Allardyce suggested that City's long trip to Moscow in the Champions League could favour his side ahead of Saturday's lunchtime clash.
He added: "We've got a different team to when we played Man City last season. They're a fabulous side but if we're going to challenge them at any time this season this might be it, coming off a Champions League game. If we can keep their superb attacking force quiet we'll then have to see if we can exploit any weaknesses.
"We've scored 15 goals in our first eight games and our total last year was 40. It shows what goalscorers can do."