And they should be even higher too.
A deserved victory was snatched away from them at fierce rivals Chelsea last time out when a phantom penalty was awarded to the Blues in the 89th minute allowing them to salvage a 2-2 draw.
Those extra two points would have seen the Hammers leapfrog Manchester City into fourth place and just three points off third-placed Arsenal.
Even Chelsea boss Guus Hiddink backed the Hammers for the top four (see video).
Eyes on two prizes
Of course the Champions League places isn't the only thing Bilic's side have to play for with the small matter of an FA Cup quarter-final replay against Manchester United at the Boleyn Ground on the horizon.
But one crucial fact could mean the Hammers' hopes of dining at Europe's top table will be very much a reality.
No fewer than five of West Ham's last eight league games are at home, two of them being under the famous lights at Upton Park.
Three of those games are against teams in the bottom half namely Crystal Palace, Watford and Swansea while the other two, against Arsenal and Manchester United are potential Champions League six-pointers.
'We fear nobody'
"It's great that with eight league games to go five are at home and only three away," Sullivan told whufc.com.
"We fear nobody at the Boleyn Ground having been unbeaten since August."
West Bromwich Albion, leaders Leicester City and Stoke City await on the road.
Win one or two of those and four of their home games and the Hammers will be more or less guaranteed a top four spot.
Not that settling for a Europa League place would be a failure in any way, shape or form for the reinvigorated East Londoners.