O'Neil, who is also out of contract in the summer, says owners David Sullivan and David Gold should look no further than Big Sam.
When asked about talk that Allardyce's position might be under threat, the midfielder said: "That shocks me - the gaffer has done a fantastic job.
"You see the teams who went down last year and how they've struggled to bounce back, like Bolton and Wolves.
"To get us back up and then keep us clear of relegation so far, he has done a fantastic job. The lads all love working for the gaffer and we're just trying to do the best job we can for him."