However, the former Newcastle manager played it down by saying he does not need the security of a new deal at Upton Park.
The Hammers clinched promotion to the top flight via the play-off final on Saturday as they beat Blackpool 2-1 at Wembley, although the Seasiders should have been 3-0 up at half-time.
Allardyce, who arrived at the club last year, is out of contract next summer and has not been handed a new deal.
Allardyce: "I don't need the security of a contract to work in this game as far as I'm concerned. I'm my own man now.
"Somewhere down the line in the middle of next year, maybe, but not now."
Hammers co-owner David Gold: "There are no talks planned but Sam's our manager for the foreseeable future.
"There's no pressure, he's got a great contract."