The Senegalese international hit back at critics of Allardyce's perceived negative approach.
Diouf said: "If Sam goes there they'll eventually reach the Champions League.
"He is a man who with zero can be the best. They need a character.
"With Bolton we played champagne football with Hierro, Campo, Okocha and myself."
Allardyce will pocket £100,000 per week after being tasked with saving the Toffees.