Todd Graham, Arizona State head coach. Graham has had tremendous success at nearly every coaching stop he's made, and he's made a lot of them. After taking Rice to a bowl, Graham won three conference titles in four years with Tulsa. After one 6-6 season with Pitt, he's built Arizona State into a Pac-12 South powerhouse and is looking at a potential second straight 10-win season with the Sun Devils. Would he want to continue his reputation as a job-hopper?

Steve Spurrier, South Carolina head coach. At the very least, the Head Ball Coach will be talked about in this search. One of the greatest coaches in college football history, Spurrier was Florida's head coach from 1990-2001, winning the school's first six SEC championships and its first national title. After leaving the Gators for an unsuccessful stint with the Washington NFL team, Spurrier has become South Carolina's all-time winningest head coach, but FootballScoop reportshe might accept an offer to return, if it's made.

Gary Patterson, TCU head coach. Patterson has been at TCU since the turn of the century, transforming the Horned Frogs from a small-conference powerhouse to a national contender. He's a defensive-minded coach, which might be a red flag after Muschamp, but his TCU team is fifth in the country this season with 45.9 points per game.

A Stoops. Mark Stoops, the former defensive coordinator for Florida State, the youngest of the three coaching brothers, has engineered a swift turnaround at perennial SEC bottom-feeder Kentucky. The Wildcats have recruited well under Stoops, bringing in a top-25 class last year including four of the top five in-state prospects, and are a win away from their first bowl game since 2010.

His brother Bob, the head coach at Oklahoma, is a former Florida coordinator, but has long been considered a potential NFL name. (He said Monday that he doesn't want to be considered a candidate.)

A hot-shot coordinator. Clemson's Chad Morris, Alabama's Kirby Smart, and Michigan State's Pat Narduzzi are names commonly brought up for coaching vacancies big and small. But it's hard to imagine Florida going with a coordinator and first-time head coach again after Muschamp's disastrous tenure.

A longshot from a small program. Justin Fuente has built a solid program at Memphis, but a winning season this year is his first as a head coach.

Undefeated Marshall is led by Doc Holliday, who has plenty of Sunshine State ties, but he's a West Virginia native, for what that's worth.

Jim McElwain will be a popular name for big coaching vacancies after building Colorado State into of the nation's best mid-major programs, but it's unlikely Florida will hire another Nick Saban guy.

Mark Hudspeth was a hot coaching commodity last year after his third straight nine-win season, but the Ragin' Cajuns haven't been quite as dominant as expected despite an undefeated record in Sun Belt play.

There's an FCS longshot as well -- Ron Roberts at Southeastern Louisiana, who has ties to the region and a 71-28 record as a head coach.

[Update: ESPN reports Monday that the following two coaches will not be considered, so we've moved them down here.]

Dan Mullen, Mississippi State head coach. The hire that makes the most immediate sense. Mullen is a former Florida coordinator who has success as an SEC head coach. Mullen was on Urban Meyer's Notre Dame staff before becoming his quarterbacks coach at Bowling Green and Utah. At Florida, he ran an offense that won two national championships in four years. He has taken Mississippi State to five straight bowl games, including a potential Playoff spot this season. But FootballScoop is reporting there may be "something between" Mullen and athletic director Jeremy Foley that would prevent this from happening.

Rich Rodriguez, Arizona head coach. He may not have SEC ties, but Rodriguez's transformation of the Arizona program into a Pac-12 contender has him as one of the hottest prospects in the country. That's happened before -- his three straight double-digit win seasons at West Virginia got him hired by Michigan in 2008 to replace Lloyd Carr. The Wolverines went 15-22 in his three-year tenure, and his poor record at the only powerhouse he's coached at could scare the Gators away, if he's even interested in starting over again.

[Update: Pat Dooley is reporting Gundy will not be a candidate for the position.]

Mike Gundy, Oklahoma State head coach. A former OSU quarterback, Gundy took over for Les Miles before the 2005 season and is a win away from nine straight bowl appearances. The Cowboys have won at least 10 games in three of the past four seasons. He's almost exclusively coached in the Big 12, with a combined four years at Baylor and Maryland, and may want to continue building at his alma mater. But he reportedly considered the Tennessee job a couple years ago. Bovada listed Gundy as the favorite. For what it's worth, Bovada had Charlie Strong as the Texas favorite last year.