Hammers' co-chairman David Gold confirmed on Sunday that any talks over a new contract for Allardyce will have to wait until Premier League survival has been assured.
Allardyce, 58, guided West Ham back to the top flight last season after replacing Avram Grant at the helm and has taken the Hammers to 11th in the Premier League with just 12 games remaining.
A 2-1 defeat at struggling Aston Villa on Sunday was followed by a statement from Gold saying Allardyce was still the man to lead the Hammers forward and the manager himself was in bullish mood.
"I know my relationship with David Sullivan and David Gold well and the conversations that we have remain confidential," he said.
"I'm more than happy to do the job that I'm doing right now and speculation regarding my contract situation has nothing to do with anybody else but the owners."
Hammers skipper Kevin Nolan backed Allardyce to comfortably lead the east Londoners to top-flight safety.
"We still want to get more points to get safe, but we are in a good position," he said. "We would like to be where we are, the position we are in now, not with the teams scrapping at the bottom.
"We have to just make sure we keep our noses in front and are picking up the results at home, and then as many as we can get away.
"We are looking upwards, making sure we are top of the pile of the teams we are currently on top of. We want to keep pushing still for that top 10 place, as that is where we want to be and is where we know we can be."