Meanwhile Chelsea have endured a torrid start and languish in 12th place.
Enforced change to winning team
Former Croatia boss Bilic will have to make changes to the team which beat Crystal Palace 3-1 last time out, though, because loan star Victor Moses is ineligible to play against his parent club.
Moses, who signed a new four-year deal at Chelsea before joining the Hammers on a season long loan, was key in the victory over his old side Palace and will be a big miss.
One thing about West Ham this season, though, is that for once they have the squad to cope.
Co-owners David Sullivan and David Gold were true to their word of investing significantly in the squad over the summer, bringing in 12 players.
What are Bilic's options?
So what are Bilic's options to replace Moses for the East vs West derby?
Well the Hammers have been far less convincing at the Boleyn Ground than on their travels and probably needed to take a different approach at home.
Skipper Mark Noble will be grateful Moses cannot play because he would have been the player most likely to drop out given his poor recent form.
Spanish midfielder Pedro Obiang, who has impressed in the game time he has had for the East Londoners so far, could come in but it would probably force another key player Manuel Lanzini to play out wide on the left.
That would be a shame given how good he has been in his preferred central position linking up with Dimitri Payet.
Zarate, Carroll or Jelavic?
Mauro Zarate, who played a key role in West Ham's second and third goals when coming on as a second half substitute against Palace, could come in.
While Zarate often holds onto the ball for too long, his 15 minute match-winning cameo against Palace may well persuade Bilic to use him in Moses' absence.
A change of formation could see Bilic bring in either Andy Carroll, who set up the winner against Palace, or Nikica Jelavic to partner Diafra Sakho and perhaps that is what is needed to improve their Upton Park performances.
Valencia or Antonio?
Another option Bilic could look at is bringing back Enner Valencia in a left-sided role as like Moses he offers blistering pace.
Valencia also has good memories of playing against Chelsea last year when he gave Blues defender Branislav Ivanovic a torrid time.
He scored in West Ham's Under 21 side's game against Wolverhampton Wanderers on Monday night where he was taken off after 45 minutes, presumably with a view to being involved in Saturday's squad.
The least likely change but perhaps the most logical would be to bring in new £7 million winger Michail Antonio who has only featured once as a substitute since signing from Nottingham Forest.
A very similar player to Moses and blessed with pace, skill and an eye for goal Antonio could be a surprise inclusion which may catch Blues boss Mourinho on the hop.
However, he was left out of West Ham's squad altogether last time out against Palace so that looks unlikely.