The Hammers boss believes that Grant will not be given a lot of time by owner Roman Abramovich to deliver trophies.
Speaking in the Daily Mirror he said, "Unless you get results and success quickly then you don't get the same time anymore.
"Everything Avram Grant does is going to be analysed and that is something he has to handle.
"If you are lucky enough to be a manager of a top-four club then that comes with the territory."