Fisher arrived at the team complex Tuesday morning aboard owner Stephen Ross' helicopter. He's believed to be the Dolphins' top choice, but competition from other NFL teams might be fierce.
The Dolphins are looking for a replacement for Tony Sparano, who they fired on Dec. 12.
The team announced Monday it had completed an interview with interim coach Todd Bowles, and two other lesser-known candidates have been linked to the job. A league source told La Canfora on Monday that the Dolphins will interview Chicago Bears special teams coordinator Dave Toub on Tuesday and Wednesday. The New York Daily News reported the team also is interested in New York Jets defensive coordinator Mike Pettine.
Sources told La Canfora that the Dolphins are running two separate coaching searches, with ex-Kansas City Chiefs president Carl Peterson leading the charge for Fisher and current general manager Jeff Ireland compiling a list of less-experienced and less-powerful candidates. Peterson could be given the position of team president if Fisher lands in Miami, according to the sources, putting Ireland's status in doubt.
Fisher, who compiled a 142-120 record in 17 years as coach of the Houston Oilers/Tennessee Titans before sitting out the 2011 season, also is a leading candidate to replace Steve Spagnuolo in St. Louis, according to La Canfora.
Fisher has a career record of 142-120 (.542) and led his teams to at least 12 wins four times. He coached more games for one franchise than all but six coaches, all Hall of Famers.
The Dolphins (6-10) missed the playoffs for the ninth time in the past 10 years. The losing season was their third in a row, the franchise's longest such stretch since the 1960s.
The Associated Press contributed to this report