Les Miles and Kansas have spoken about the program's open head coaching job, sources tell CBS Sports. There seems to be mutual interest between the parties.

Miles was listed by CBS Sports as a top candidate at KU earlier this week. However, at that time, the two sides had not yet spoken.

Kansas athletic director Jeff Long said Sunday that he prefers "an experienced head coach" to replace David Beaty. Long also said he wants to hire a replacement "sooner rather than later."

A FlexJet plane from Dallas carrying Long and Kansas deputy athletic director Sean Lester landed in Lawrence, Kansas, about approximately 6:20 p.m. ET. According to sources, it was scheduled to depart from Dallas to Baton Rouge at some point on Thursday but that flight was cancelled. 

Recruiting pressures related to the Dec. 19 early signing period could have factored into his decision to fire Beaty with a month left in the regular season.

"There really isn't a frontrunner," Long told reporters on Sunday. "I'm going to be looking for a leader of young men, someone who has maybe a history and track record of building a program, because we have to build a program and it's really important to do that."

Miles, who turns 65 on Saturday, was one of the nation's top coaches during his 12 years at LSU. He won 77 percent of his games and led the Tigers to a pair of SEC titles and the 2007 national championship.

Miles played offensive line for Bo Schembechler at Michigan in the mid-1970s. He and Long worked together at Michigan as assistant coach and associate AD, respectively, from 1988-94.

Prior to joining LSU, Miles was 28-21 in four seasons at Oklahoma State, beating Bob Stoops' Oklahoma teams in back-to-back seasons. That turnaround with the Cowboys was at least similar to the Kansas situation. When Miles arrived in 2001, Oklahoma State had losing seasons in 11 of the previous 12 years.

Miles has indicated in the past he would switch to a spread offense, if need be, at his next job. He ran a ground-based pro-style attack at LSU.

Sources indicate Kansas will pay a commensurate salary for the right candidate and will beef up staffing around the football program.

Industry sources have indicated that certain candidates could have enough leverage to get a six- or seven-year deal from Kansas considering the state of the program and the scope of the turnaround.

Beaty is currently 6-39 nearing the end of his fourth season; he agreed to stay on for the remainder of the 2018 campaign. Kansas hasn't had a winning season since 2008. This season, it snapped a nine-year road losing streak.