The 63-year-old was appointed as manager in November to help steer the Toffees out of relegation trouble, a mission which has been accomplished.
However, the Everton fanbase has not fully taken to Allardyce, with terrace chants and banners calling for his departure being heard and seen in recent months.
"I would have thought there will be some meeting somewhere along the line next week," Allardyce, who has a season remaining on his contract, told The Guardian.
"I would think it will be with Farhad [Moshiri, co-owner]. It depends on what part of the world he's in. He's a busy man, running companies worth billions and billions of pounds. His schedule is far greater than mine so I'll drop into his schedule whenever I possibly can and meet him where I can, if that is what he wishes.
"He has got things to sort out. We all have things to sort out. At the moment for me it is speculation and I will find out what Farhad is thinking when I see him. I can't speculate or predict what Farhad is thinking or isn't thinking. I've done all I can do, that's what I'll say to him – I can't do any more than that.
"Right now the players will be speculating, as will the staff, as will everybody. Speculation is one of the worst things to happen in a football club results-wise because when it starts – and there's a lot of speculation about me, about players and about everything else – it's difficult."