But Nutt said Sunday afternoon he believes it's "just talk" and hasn't been contacted by the school.
The New Orleans Times-Picayune mentioned the seventh-year coach as a possible candidate, reporting that "perhaps someone on the level of Oklahoma State coach Les Miles or Arkansas' Houston Nutt might be interested" in the job.
Saban, who guided LSU to a national championship last year, announced Saturday his decision to leave the Tigers after five seasons to take over as Miami Dolphins coach.
"I've had no contact whatsoever with LSU," Nutt said. "I think it's just talk. I think it's all just rumors and rumors of.
"It sounds like nothing to me."
Arkansas athletic director Frank Broyles did not return calls Sunday night.
LSU athletic director Skip Bertman said Saturday the school's coaching search would begin immediately and hopes to have a new coach in place in the next couple of weeks. LSU has hired a search firm to gauge the interest of coaches that have tossed their name into the hat for what should be a coveted job.
Other names that have emerged as potential candidates are former Cleveland Browns coach Butch Davis, San Francisco 49ers coach Dennis Erickson, Louisville coach Bobby Petrino and LSU offensive coordinator Jimbo Fisher. LSU's opening is considered a premiere position after Saban restored the Tigers during his tenure, leading them to two Southeastern Conference championships and last season's 21-14 win against Oklahoma in the Bowl Championship Series title game.
Saban and Nutt are represented by the same agent, Jimmy Sexton, who didn't return calls Sunday.
Sexton, a Memphis-based agent, was a key player in Nebraska's courtship of Nutt last year, helping the Arkansas coach negotiate with both sides.
Nutt eventually turned down an offer from the Cornhuskers and was given a raise at Arkansas, bumping his salary to approximately $1.4 million a year.
"I know Jimmy hasn't talked to (LSU) about me" Nutt said. "I don't think it's anything."
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