She would have become the first woman to interview for an National Football League head-coaching job.
"She's an unbelievable person", the source said. He says the team's "coaching search will be thorough and deliberate" and Rice "has not been discussed".
A Cleveland Browns helmet rests on the field prior to the game against the Philadelphia Eagles at Lincoln Financial Field on September 11, 2016 in Philadelphia, Pennsylvania.
Their win over the New York Jets in September was the team's first in 635 days, but one win and three defeats in the games that followed led to Jackson's sacking.
Image The Cleveland Browns have struggled for form this season
Rice's last reference is common among die-hard Browns fans, who still bemoan then-coach Marty Schottenheimer's decision to play soft coverage in the 1986 AFC championship game when Denver quarterback John Elway drove the Broncos 98 yards to a game-tying touchdown in the final seconds.
"I just want the best possible head coach to move this thing forward regardless of age", Dorsey said.
Ms Rice - who served as the state secretary during the second term of president George W Bush - is a notable Browns fan, but has no experience in professional sports. "It could be a woman, too. I'm serious. We're going to look at everything". According to ESPN, the Buffalo Bills, the Oakland Raiders, and the San Francisco 49ers have all recently added women to their coaching staff.
But after the story broke, the Browns general manager insisted that Rice was not being considered for coach.More news: Texas sneaks into top 15 in latest College Football Playoff rankings
More news: Harvard scientists say mysterious space object may be from ‘alien civilization’
More news: Recount Likely in Florida Governor Race