The Hammers are winless this season and lost 1-0 to Wolves on Sunday.
Pellegrini was only drafted in during the summer having been managing in China.
But Cascarino reckons his days at club could already be numbered having spent an eye-watering £100m during the transfer window.
He wrote in The Times: “Last year I said after four games that Frank de Boer had to get the sack at Crystal Palace and I've got the same feeling with Manuel Pellegrini at West Ham. Given the way they are getting beaten, I cannot see a way out for this team."