"It's not going to happen," Peterson told The Associated Press on Wednesday. "I have a lot of good friends there, but I need to get away for a while. It's been 20 years of making decisions every day and I need a rest."
Peterson resigned on Dec. 15 after a 20-year run as president, general manager and CEO of the Chiefs and is a good friend of Stephen M. Ross, who is buying the Dolphins.
In a 40-minute farewell speech to friends and Chiefs staff Tuesday, Peterson said he does not intend to retire. Afterward, he declined to address whether he had plans to work for the Dolphins and said that heading to Miami was "pure speculation and I don't deal in speculation."
Ross's purchase of the Dolphins from Wayne Huizenga is expected to conclude soon. Ross owned the highly successful USFL team that Peterson ran, and the two have remained close.
Peterson is also close to Jeff Ireland, the Dolphins general manager who got his start in the NFL as a Chiefs scout under Peterson.
"I have a 25-year friendship with Stephen Ross," Peterson told the AP. "But I have no plans to do anything right now but rest."
There has also been speculation about the future of Dolphins boss Bill Parcells, whose regime produced the turnaround that resulted in the franchise's first playoff berth in seven years. His contract allows him to leave the Dolphins and still collect the $9-12 million remaining on the four-year deal if the team is sold.
But following Sunday's loss to Baltimore, Huizenga said Parcells told him he plans to remain executive vice president of football operations. Ross has said he wants Parcells to stay.
Chiefs owner Clark Hunt is interviewing candidates to replace Peterson, who won four AFC West titles and had three 13-win seasons with the Chiefs. Hunt has spoken with New England Patriots executive Scott Pioli, among others, and is paring down a lengthy list of candidates.