Rice would become the first woman to interview for an NFL head coaching job.
When discussing the vacancy last week, Cleveland general manager John Dorsey said he was open to hiring a woman.
The interview process could even lead to Rice becoming involved in the organization in another capacity, such as a consultant, according to Schefter.
"She's an amazing person," a team source told ESPN.
The Browns issued a statement denying their reported interest in Rice shortly before kickoff Sunday.