The 21-year-old has a contract with the Hammers until the summer of 2024 but Cottee insists Rice could decide to run his deal down and walk away on a free.
Rice has been flirting with a move back to Chelsea, where he spent eight years in the youth setup, since the appointment of Frank Lampard as manager.
Lampard is said to be yearning to bring in his compatriot to complement N’golo Kante as a double pivot in midfield and Rice could also be deployed as a center-back when the need arises.
West Ham are reluctant to sell one of their prized asset but potential suitors could force the East Londoners to sanction the sale of Rice if there is a tempting offer.
Cottee has urged the Premier League side to vanquish that threat by putting a fresh deal for Rice, and insists similar thing should be done with head coach David Moyes, who has rejuvenated the side this season.
“As far as I’m concerned the only two signings to be bothered about are David Moyes and Declan,’ the former West Ham striker told The Sun.
“I’m pretty sure that even now, with his elevated status, Dec will not be earning the same kind of money as the top men in the squad.
“But he’s their most valuable player and in time will become the next captain after Mark Noble.
“I know he signed a five-year deal not so long ago but get him tied down and up there with the bigger earners and make him a bedrock of the future team.
“We all know other teams are interested. West Ham should be acting to secure Declan, so he is not allowed to drift into the last two years of his contract and possibly leave on a free transfer."
