The team later confirmed that it is finalizing a deal to hire the 53-year-old Fisher.
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Fisher had been the most prominent candidate connected to any of the current head-coaching vacancies, interviewing with both the St. Louis Rams and Miami Dolphins. Most recently, NFL Network had reported that Fisher was close to joining the Dolphins. Previously, NFL Network insider Jason La Canfora had reported that St. Louis was likely to hire Fisher, but later reported that compensation had been an issue between Fisher and the Rams, with Fisher wanting about $7 million per season.
He interviewed twice with the Rams, once in Denver with owner Stan Kroenke and again in St. Louis when he toured facilities and met with quarterback Sam Bradford.
"The process has been lengthy, but for good reasons," Fisher told the St. Louis Post-Dispatch on Friday. "I took a lot of time looking at and exploring in detail the non-economic issues of both clubs."
A Dolphins source told NFL.com's Jeff Darlington following Fisher's decision to go to St. Louis that he never asked for complete control over the Dolphins. According to the source, Fisher expressed during the interview that he wanted a mutual decision-making process with general manager Jeff Ireland, which is what the Dolphins also planned to institute.
St. Louis' offer might have trumped Miami's for several reasons. The Rams have former No. 1 overall pick Sam Bradford at quarterback, the No. 2 overall pick in this year's draft and a favorable salary-cap situation. In addition, chief operating officer Kevin Demoff is the son of Fisher's agent, Marvin Demoff.
"I'm pumped," fullback Britt Miller told The Associated Press.
Receiver Brandon Lloyd, who will become an unrestricted free agent this offseason, told NFL Network that Fisher "brings a lot of stability and I think that's what the players are really crying for."
Fisher also spent a season with the Rams as defensive coordinator in 1991, when the franchise was based in Los Angeles.
He stepped down from his position with the Titans a year ago as the league's longest-tenured coach, saying he needed a break, and sat out the 2011 season.
The Dolphins will now likely turn to one of the other candidates mentioned in connection with their vacancy, including interim coach Todd Bowles, Cincinnati Bengals defensive coordinator Mike Zimmer, Green Bay Packers offensive coordinator Joe Philbin and Chicago Bears special teams coordinator Dave Toub. Bowles has also been mentioned as a candidate for the Oakland Raiders' head-coaching job.
The Dolphins already have an interview lined up for Saturday, a team source told Darlington, but the source would not reveal the name of the candidate. It is not a "big name" in the category of guys like Jon Gruden or Bill Cowher.
The Associated Press contributed to this report.