The 58-year-old has been in charge at Upton Park since last summer and guided the Hammers back into the Barclays Premier League at the first time of asking.
Co-owner David Gold released a statement on Sunday saying contract talks with Allardyce will not open until top-flight safety has been assured, with West Ham currently seven points clear of the relegation zone.
"As David Sullivan and I have always maintained, we will sit down and discuss Sam's contract situation once our Premier League status has been confirmed and not before," Gold's statement read.
"This is purely because the three of us don't want anything to distract attention from our aim of finishing as high up the Premier League table as possible."
Allardyce saw his side slip to a 2-1 defeat at struggling Aston Villa on Sunday and was in bullish mood when asked about his contract talks.
"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."