West Ham manager David Moyes doesn't believe Champions League qualification is "in their own hands".
The Hammers beat Leicester 3-2 last weekend to return to the top four with seven games to play.
West Ham are away to Newcastle on Saturday knowing a win would move them up to third place and guarantee they head into next weekend's clash with Chelsea above their London rivals.
Declan Rice and Michail Antonio will both miss the trip to St. James' Park, while Aaron Cresswell is a doubt.
When the Magpies won 2-0 away to West Ham on the opening weekend, few would have predicted the turnaround in fortunes for Moyes.
West Ham finished four points off the Champions League places in the 2015/16 season but this season represents a much better opportunity to secure a place in the top four.
Moyes admits it's hard not to dream the closer they get to the finish line.
"This is the third time this season we have gone fourth, I think, and when you are beginning to touch you you start to think we can do it," Moyes said in his press conference.
"Chelsea, Liverpool, Tottenham, Everton are all teams that can touch us. We have seven to go I have my targets and the players know what we need to do.
"I said to the staff you don't get many opportunities to do it so we have a chance but I know that we are not favourites with the boookies.
The former Manchester United boss was asked if he would be disappointed if they don't finish in the top four.
"Would I be disappointed? Of course, I would be.
"We are competing really well and we are trying to keep putting on shows and pulling out results but I am not putting expectations that we are going to make the Champions League as that is not fair on the players who people probably thought they would be just outside the bottom three.
"But deep down if we do not keep pushing the other teams hard we would be disappointed."
West Ham play Chelsea next weekend and then have games against Burnley, Everton, Brighton, West Brom and Southampton.
Moyes is trying to play down the significance of that game against Chelsea.
"I don't see it being that big, to be honest, we are just trying to beat whoever we are against.
"We are not sitting here thinking about Chelsea or Liverpool.
"The position we are in is terrific but we can only think about Newcastle at the weekend.
"We feel as if we have to win our games and, if we do that, it’ll give us a chance.
"We’re ahead of Liverpool, Chelsea and Tottenham at the moment, and it’ll be hard to stay above clubs like that, but we’ll take one game at a time and see where we end up."