The Tennessee Titans have Fisher under contract for 2007 after owner Bud Adams picked up an option on his coach, and the team is working on a long-term extension.
"We haven't been contacted by Dallas," chief executive officer Steve Underwood said in a statement Tuesday. "In the event that we were, there are no circumstances that we would grant permission to the Cowboys to speak with Coach Fisher."
With the resignation of Bill Cowher from Pittsburgh on Jan. 5, Fisher is the NFL's longest-tenured coach with one team. He has spent 12 full seasons with the Titans, a tenure that started with six games in 1994 coaching the then-Houston Oilers with a 110-97 record.
Fisher also helped guide quarterback Vince Young to AP Offensive Rookie of the Year honors and an 8-8 record after an 0-5 start. Fisher is taking part in interviews for the team's next general manager who will replace Floyd Reese, who resigned on Jan. 5.
Even if Adams might not mind letting Fisher leave, Dallas would be the last team he would let steal away one of his coaches. Adams still lives in Houston where his Oilers fought to attract attention away from the Cowboys in Texas before relocating to Tennessee in 1997.
Meanwhile, the Cowboys commenced the search for a successor to Parcells on Tuesday, beginning what figures to be an expansive process by interviewing three in-house candidates.
Owner Jerry Jones met with assistant head coach Tony Sparano, secondary coach Todd Bowles and wide receivers coach Todd Haley. The Cowboys are also seeking permission to speak with Chargers defensive coordinator Wade Phillips.
While none of the three possesses the kind of high profile Jones is likely to seek, all have merit and all were held in high regard by Parcells.
A six-year NFL veteran, Sparano, 45, might have the most legitimate shot of the three, given that he worked closely with quarterback Tony Romo and called most of the plays on offense. Dallas this week denied at least one other NFL team permission to speak to Sparano about a vacancy on its staff.
Sparano served as head coach at New Haven (1994-98), where his teams made two trips to the NCAA Division II playoffs and lost in the 1997 championship game. His NFL resume includes stops at Cleveland (1999-2000), Washington (2001) and Jacksonville (2002). He joined the Dallas staff in 2003.
A former NFL defensive back, Bowles, 43, played eight seasons for the Washington Redskins (1986-90, 1992-93) and San Francisco 49ers (1991). He has six years of experience as an NFL assistant coach and, had Parcells returned in 2007, likely would have been promoted to defensive coordinator to replace the departed Mike Zimmer.
Interviewing Bowles, an African-American, means the Cowboys have met the stipulations of the Rooney Rule, which mandates a team must interview at least one minority candidate.
Haley, 39, worked on Parcells' staff with the New York Jets, his first job in the league. He was on the Chicago staff after that, before he reunited with Parcells in Dallas in 2004. Haley is a potential candidate for the offensive coordinator position with the Arizona Cardinals.
Sources tell ESPN's Ed Werder that Jones has made contact with former Dallas backup quarterback Jason Garrett about possibly becoming the offensive coordinator under whomever Dallas hires to replace Parcells.
The Cowboys first received permission from the Miami Dolphins, who have Garrett under contract as their quarterbacks coach for one more season. The Cowboys are making hires that will accelerate the development of Romo and are believed to be considering pairing Garrett with either Phillips or 49ers offensive coordinator Norv Turner. Both have previous head coaching experience.
Turner was the Cowboys offensive coordinator when Troy Aikman led the Cowboys to back-to-back Super Bowl titles in the 1990s. Garrett was Aikman's backup. In addition to being so instrumental in Aikman's career that he was the quarterback's Hall of Fame presenter, Turner has also been involved in the development of Drew Brees in San Diego and, currently, Alex Smith in San Francisco.
Information from The Associated Press and ESPN.com senior writer Len Pasquarelli was used in this report.