ESPN's Adam Schefter, citing a league source, reported Sunday that the Browns would like to interview Rice for the open job.
Rice, who is a Browns fan but has no football coaching experience, did not explicitly turn down the opportunity but said she was "not ready" to coach.
"I love my Browns -- and I know they will hire an experienced coach to take us to the next level," Rice said in a statement.
Statement from GM John Dorsey: pic.twitter.com/aQExOzX0ge— Cleveland Browns (@Browns) November 18, 2018
She would be the first woman to be interviewed as head coach.
"On a more serious note, I do hope that the NFL will start to bring women into the coaching profession as position coaches and eventually coordinators and head coaches. One doesn't have to play the game to understand it and motivate players. But experience counts -- and it is time to develop a pool of experienced women coaches," she said.
"BTW -- I'm not ready to coach but I would like to call a play or two next season if the Browns need ideas! And at no time will I call for a 'prevent defense.' "
Browns general manager John Dorsey also said in a statement that the architect of former President George W. Bush's foreign policy has not been discussed as a Browns coaching candidate.
Rice is "a great leader, possesses the highest possible character and also happens to be a Browns fan," Dorsey said. "I have the utmost respect and admiration for all she's accomplished and was honored to meet her for the first time earlier this season.
"Our coaching search will be thorough and deliberate, but we are still in the process of composing the list of candidates and Secretary Rice has not been discussed."
Though it's unlikely that a newbie would be hired to a major coaching position, Rice does have experience in executive roles in sports. She was a member of the College Football Playoff selection committee for three years, and she chaired a committee that proposed changes to NCAA basketball.
The Browns, one of the worst teams in the NFL over the past decade, fired coach Hue Jackson two weeks ago. He won just three out of 40 games over two and a half years with the team, so there's almost nowhere to go but up.
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