Allardyce has faced speculation over his future for much of the season amid persistent criticism from some of the club's supporters.
One newspaper this week claimed West Ham's owners have already taken the decision to seek a new manager once Sunday's final game at Manchester City is out of the way.
But Allardyce is on the brink of delivering a second successive mid-table finish and is continuing to plan for next season until told otherwise by owners David Sullivan and David Gold.
He said: "I spoke to David Sullivan on Thursday about us arranging our usual meeting to go through pre-season budgets and what's going to happen next season, and I had no indication about my position being under threat.
"That's all I can say, that's all I know, and he's the boss. That's the bottom line for me.
"I rang him up, spoke about what was being bantered around, and under those circumstances we talked about getting together and having our meeting next week.
"Has the speculation undermined my position? I'm not so sure about that. People in the game have to write speculation about what's happening at certain clubs because they have to sell papers.
"Whether it's right or wrong only time will tell. Speculation's part of the game, whether that speculation becomes a reality at this moment in time we don't know. I will find out next week."
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