Sullivan apologised for the campaign at the club's end-of-season awards dinner on Tuesday night.
Allardyce is due to meet Sullivan next week but the Hammers boss does not believe his position will be on the agenda.
"I rang him up and spoke to him about what's been planted around and under those circumstances we just talked about getting together and having our meeting next week," Allardyce said.
"The only thing I can say is I spoke to David Sullivan yesterday about us arranging our usual end-of-the-season meeting to go through pre-season and go through budgets and what will happen next season.
"I had no indication that my position is under threat. That's all I know, he's the boss and that's the bottom line for me."
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