A new-look West Ham get their season underway with a trip to Merseyside to face last season's Champions League finalists, in what will be Pellegrini's first game in charge.
The Chilean has brought in eight new players this summer, including Lucas Perez from Arsenal on transfer deadline day for what is believed to be a bargain £5million.
Rice, 19, broke into the West Ham side under Slaven Bilic but really made an impact during David Moyes' time at the London Stadium - almost becoming the club's first-choice central defender. Cottee believes the 6ft 1in ace must start.
“Rice needs to be playing,” Cottee said. “The fans will demand that. They won’t accept it if players like Declan get squeezed out. We have some great young talent and that needs to come through.”
Pellegrini has given himself plenty of selection dilemmas by bringing in Lukasz Fabianski, Ryan Fredericks, Issa Diop, Fabian Balbuena, Andriy Yarmolenko, Jack Wilshere and Felipe Anderson.
Rice will be in direct competition with Balbuena and Diop for a start at the centre of defence, along with Angelo Ogbonna and Winston Reid. Though Pellegrini could use the Republic of Ireland international in the middle of the park.