The Liverpool legend is not sure if West Ham should send Big Sam on his way.
Allardyce is out of contract in the summer and there is a growing sentiment from a group of West Ham fans that he should not have that deal extended.
The Hammers boss has done well with West Ham in his time at the club and at the start of the season looked to have really turned a corner.
But they have been poor in 2015 and those fans have ammunition once again.
Carragher doesn't understand why the West Ham fans are not keen on an Allardyce stay, but he believes they should be worrying more about staying in the Premier League - which Allardyce would surely guarantee:
"The fans have never really taken to him considering what he's done for the club. They will claim his style of football isn't good enough, or the fact they don't have that maverick player from the past within the squad.
"But with Sam Allardyce, you don't go down, you'll always do well in the Premier League, you'll stay up and, with the Olympic Stadium coming, I would think West Ham would want to keep a manager who could achieve that because in the past, they have been relegated at different times.
"However, sometimes clubs and managers simply don't fit."
West Ham fans want to see their team push on and staying up is not necessarily their number one target. They want European football and regular top ten finishes, as well as a more 'West Ham' style to their play.