Allardyce said that it is up to the club's board whether they decide to stick with him, but at the moment he is concerned only with beating Sunderland on Saturday.
"I wouldn't have thought I'd need any discussions with the owners, they're either going to stick with me or they're not," BBC Sport quotes Allardyce as saying.
"That's entirely up to them depending on how they see the situation at the moment. Everyone will speculate about my position because I'm around where all the other clubs are and all the other clubs have got rid of their managers.
"It's about picking a few results up and then the pressure goes away for a while. It's the first time in two-and-a-half years that we've had a bad run since I've been here. It happens, we've got to make sure we're determined enough and have the right desire to overcome it."
West Ham are currently 17th after just one win in eight.