Speaking to the Daily Express, Cottee - who scored 115 league goals for the Hammers - was unequivocal, saying: "Rice needs to be playing. The fans will demand that," he said.
West Ham have enjoyed a successful summer transfer window, signing no fewer than nine new players - including two centre backs, Fabian Balbuena and Issa Diop.
However, Cottee warned that this was not a good reason to sideline Rice, who featured in 26 clashes for the Hammers in last season's Premier League campaign. "They [the fans] won’t accept it if players like Declan get squeezed out," said the former Hammers striker, adding: "We have some great young talent and that needs to come through."
Despite some unfortunate errors, Rice has generally played with a confidence and maturity that belies his years. The 19-year-old's emergence as a first team player was one of few positives for the Hammers last season under David Moyes.
The club's exciting new purchases - especially club record signing Felipe Anderson - and their impressive new manager, former Manchester City boss Manuel Pellegrini, have filled the West Ham faithful with optimism for the 2018/19 season.
However, Cottee sounded a cautionary note. "As a West Ham fan, I’m quietly optimistic," he admitted, but then he added: "A lifetime supporting the club teaches me to be cautious. We have been here before, where a lot of money has been spent and it ends in disappointment."
The 53-year-old continued: "The big problem that the manager has is managing the expectation. A lot of money has been spent, the club has gone out and got him, on big money. So the fans will be expecting big things."
If the Hammers beat Liverpool at Anfield, those expectations will only increase.