Bilic's side will be no pushover, though, having made their best start to a season in seven years and go into the match off the back of consecutive wins over Liverpool and Newcastle United.
The match pits the league's two top scoring sides together, and has unsurprisingly been selected for live coverage.
West Ham have already showed they have what it takes to beat the top teams away from home this season after convincing wins over Arsenal, 2-0 at the Emirates on the opening weekend, and 3-0 at Anfield in their last away trip.
The Blues have had a tough midweek match against Juventus in the Champions League, which delivered their first defeat of the season.
But with Manuel Pellegrini expected to welcome back Sergio Aguero from the start, City will be overwhelming favourites.
'Confident and playing without fear'
Jenkinson knows the east Londoners will have to be at their very best to get anything from the game but told West Ham's official website that the Hammers have nothing to fear.
“Of course they are flying at the moment, but we’ve got some good results against the big teams this season so we’ve got to be encouraged by that," Jenkinson said of the hosts.
"We can afford to go there with no fear at the moment, with the way we are playing this season.
"People aren’t expected to go to City and win these days and it’s not that easy, but we’ll go there confident and play with no fear.”
New attacking approach proves popular with Hammers fans
Jenkinson's attitude to the game will be popular with Hammers fans, who grew tired of seeing Sam Allardyce set up very defensively, particularly away from home.
Bilic is playing a much more attacking style and will look to frustrate City and try to hit them on the counter attack, a tactic that worked well in all three of the Hammers' wins so far this season.
Perhaps there will also be the added incentive for the on loan full back to help his parent club Arsenal by pegging their title rivals back for the first time this season.