The Tigers head coach said Tennessee coach Phillip Fulmer called him "a couple of days ago" to ask for permission to meet with Spence, who has been at Clemson three seasons.
Bowden said he wasn't the least bit concerned about the interview because, "It's just the nature of the profession."
And while he said that Spence would be on hand for the upcoming Chick-fil-A Bowl against No. 22 Auburn on New Year's Eve, Bowden said there's a real chance Spence could ultimately leave.
"I'd say anytime you go (for an interview) that it's serious," Bowden said. "Anytime you make the trip … I think once you get to that stage it's pretty serious."
Spence was more elusive than tailbacks James Davis and C.J. Spiller following practice as he dodged questions the best he could, saying only that he was "flattered."
Each time Spence or defensive coordinator Vic Koenning has spoken to other schools it has resulted in a raise.
Spence made $207,000 this season, while Volunteers offensive coordinator David Cutcliffe, who left to become the head coach at Duke, made $340,000.
However it's unclear just how much this meeting with Tennessee would increase Spence's salary at Clemson since Bowden said the new contracts for all of the assistants are done in principal.
"I have a lot to do with that," Bowden said. "I think it's pretty much solved. To the best of my knowledge it's done."
Bowden said no other schools have called asking permission to speak to any of his assistants, but added that he wouldn't be surprised if they spoke or met with other teams during the four-day Christmas break.
"I know we've got four days coming up and I'm not going to follow them around to see what they do," he said.
Should Spence leave, Bowden said already has names in mind for his replacement.
"Everybody pretty much has a short list of guys," he said. "You keep it updated."
When asked if he would fulfill the rumor that current wide receivers coach Dabo Swinney would get the job, Bowden wouldn't say.
"I'll address that when and if it happens," he said.
QUICK HITS: The team practiced in full pads Friday and had a live goal line scrimmage at the end. … Defensive tackle Dorrell Scott did not practice Friday, but Bowden said he should be fine for the first practice in Atlanta on Wednesday. …
Backup quarterback Tribble Reese completed his final practice ever at Clemson by jumping into and swimming across the moat that surrounds the practice fields. His jumping into the frigid water brought a very loud chorus of cheers from the players, while also costing some of them money who bet that he wouldn't do it.
Reese is a redshirt junior in eligibility, but has decided to that this is final year playing football.
For those wondering, Reese said that the water was, "much colder than you think." He also said that it's only about three feet deep and that the bottom was like "quick sand."
Bowden: Spence Checking Out Options
CUTigers.com Top Stories
ANOTHER CLEMSON CHAMPIONSHIP!!!#3 Clemson held on to beat #23 Virginia Tech 42-35 for its first back-to-back ACC Titles in 28 years.
CUTigers.comYesterday at 11:52 PM
ACC CHAMPIONSHIP PRESS CONFERENCEWatch Dabo Swinney's Press Conference Prior to the ACC Championship Game Between #3 Clemson and #23 Virginia Tech!
CUTigers.comYesterday at 9:38 AM
WHAT WE ARE HEARING: ACC Championship#3 Clemson looks to secure its second consecutive College Football Playoff berth by winning a record 16th ACC Title and its first back-to-back titles in 28 years!
CUTigers.comFriday at 3:06 PM
TIGERS WIN THRILLERClemson improved to 4-2 with a 60-58 win over Nebraska and helped the ACC win the 2016 ACC/Big Ten Challenge!
CUTigers.comThursday at 7:13 AM