However, Allardyce needs no reminding of West Ham's poor run of results which badly affected the club 12 months ago, picking up just one league win between the end of November and the middle of January.
"I don't think we should start predicting where we should and shouldn't be [at the end of the season]," the 60-year-old is quoted as saying by BT Sport.
"We have still got November and December to compete with and historically it has been our worst time of the season since I have been here. I am waiting till we get through that period and have a better indication on where the possibilities of where we might finish."
West Ham return to action on the weekend when they take on Stoke City at the Britannia Stadium.