Graham's retention, reported by News Sentinel partner GoVols247, adds some Southern flavor to Jones' first staff. Graham, 37, was a record-setting running back for the Vols from 1993-96 and played six years in the NFL. He spent three seasons at South Carolina before joining Dooley's staff in January.
"I'd do it again," Graham said last month of the risk he took in joining Dooley's staff. "I love my University. I wouldn't think twice about it if I had a second opportunity to do it."
The university did not confirm Saturday that the other eight assistant coaches under Dooley had been formally released, although none are expected to return.
Jones is expected to bring several assistants from Cincinnati, including some who have been with him since he first became a coach six years ago at Central Michigan.
Ideally, Jones would like to have some assistants on the ground in Knoxville before NCAA's recruiting "dead period" begins Dec. 17. During that time, coaches can call or text recruits, but can't visit with them in person.
Jones is likely to retain his two UC coordinators. Offensive coordinator Mike Bajakian has been with Jones for six years and is familiar with his fast-paced attack. Defensive coordinator John Jancek was linebackers coach and later co-defensive coordinator at Georgia from 2005-2009. He's a Michigan native who previously worked with Jones as an assistant at Central Michigan.
Receivers coach and recruiting coordinator T.J. Weist is another Michigan native with Southern experience. An Alabama grad, Weist joined Jones at Cincinnati three years ago after eight seasons at Western Kentucky.
Offensive line coach Don Mahoney is another longtime Jones assistant, who joined him at CMU after a seven-year stint at Tulane.
Safeties coach Mark Elder, who also coordinates special teams, has been with Jones for six years. He's handled running backs and tight ends in the past, so his role could be flexible if he comes South.
Cincinnati defensive line coach Steve Stripling is the interim coach, although it's unclear if he will continue to lead the Bearcats through their Belk Bowl appearance on Dec. 27 after Texas Tech coach Tommy Tuberviille was hired on Saturday. His current role wouldn't necessarily preclude Stripling from joining Jones at UT, as many coaches could juggle dual roles at both schools during the next two weeks. Tuberville told Cincinnati.com that Stripling and the current UC staff would lead the team in the bowl game.
There was so much buzz around former UT quarterback Tee Martin, now an assistant at Southern California, that Jones was even asked about him at Friday's introductory news conference.
"Obviously,'' Jones said, "he's a great coach. We all understand what he's meant to this football program. Obviously he would be an individual we reach out to, but we're going to reach out to a lot of individuals.''
Martin could have other options if he decides to return to the Southeast, and it's not clear where he would fit on Jones' prospective staff.
Jones will be provided a pool of roughly $3 million to pay assistant coaches, roughly the same amount assistants were paid under Dooley in 2012.
Graham, who joined Dooley's staff in January, was already under contract through February 2014 at a salary of $225,000.
Dooley's offensive coordinator Jim Chaney, will be paid $600,000 by Tennessee regardless of whether he finds work elsewhere. Six other assistants — offensive line coach Sam Pittman, receivers coach Darin Hinshaw, defensive line coach John Palermo, safeties coach Josh Conklin, cornerbacks coach Derrick Ansley and defensive coordinator Sal Sunseri — are collectively owed roughly $3.5 million, but they are required to make reasonable efforts to find other jobs to defray the cost of their payouts. Much of that is owed to Sunseri, the highest paid coach on Dooley's staff, who is due roughly $1.8 million through February 2015.
Jones could also bring some administrative support members to Tennessee in non-coaching roles, and strength coaches often follow coaches to new schools during these transitions.