Allardyce’s current contract with the Hammers runs out at the end of the season, and no new deal is in place.
Negotiations over fresh terms will start in the summer, but former Liverpool defender Lawrenson believes that the Englishman will not be kept in the job.
While predicting a 2-0 win for West Ham against Stoke City at the Boleyn Ground in the Premier League today, the 57-year-old wrote on BBC Sport: “I think home advantage will help West Ham edge it but, I am not sure a win will help Sam Allardyce keep his job.
“Stoke boss Mark Hughes has just signed a new contract but it looks unlikely that Allardyce will be offered one.”
West Ham started the season brilliantly, but over the past two or three months, they have faded away.
Once considered to be in contention of a top-four finish in the Premier League, the Hammers are now unlikely to even earn a Europa League spot for next season.
The London outfit have lost four of their last five matches and have won only once in their last nine.
West Ham are an ambitious club and are looking to make themselves regulars in European competitions, and Allardyce is not doing himself any favours by failing to win games.
The 60-year-old does not have a huge pedigree when it comes to taking teams to Europe, and that is likely to be taken into consideration when the West Ham bosses decide on his future at the end of the season.