"Mal Moore and Barry Alvarez," the former coach said, mentioning the athletics directors at Alabama and Wisconsin, respectively. "If you really look around the country, Barry Alvarez is running as good a program as anybody in the country because he understands."
What Alvarez understands is that football pays the freight for all of the other sports at most universities. And a healthy athletics program keeps donors happy.
"Athletics is the front porch of the university," Fulmer said. "That's how a lot of people connect."
The former Vol head man made his remarks earlier today at Knoxville's Willow Creek Golf Club, where he helped promote the second annual A3 benefit tournament that helps several Knox-area high schools through the "Play It Smart" program.
Although he has not publicly lobbied for the Vol vacancy, Fulmer is considered a leading candidate for the AD job by many observers. He is not one of those observers, he says.
"I don't even think I'll be one of the guys that they (UT brass) even consider for the thing because they're looking for a sitting athletics director more than likely," Fulmer said. "If that's the case, that's good. That's no problem.
"I'm just interested in who it's going to be."
That interest is understandable, given the instability of Tennessee's athletics department. The Vols fired head basketball coach Bruce Pearl in March and canned head baseball coach Todd Raleigh in May. Athletics director Mike Hamilton resigned in early June. Counting Fulmer's final season of 2008, the football program is 18-20 over the past three years. Moreover, NCAA penalties may be forthcoming in both basketball and football.
Clearly, Tennessee's next athletics director - whoever it might be - faces an imposing challenge.
As Fulmer put it: "I think it's one of the most important hires that's happened in our history at this particular time, to kind of help us dig out of the hole we've gotten ourselves into from a lot of fronts.
"I'm all for Tennessee and what they decide to do."
Basically, Fulmer said the next athletics director needs "some dynamics that are really important to the stability of our athletics program at a very crucial time."
Asked what those "dynamics" might be, he replied: "They need stability. They need a really, really strong leader that can understand the problems of the coaches, that can understand the problems of the university, that can communicate with coaches and fight for those things but also have a relationship with the fan base and the alumni. It takes some great skills to do that."
Tennessee's current instability is in stark contrast to the 1990s and early 2000s, when president Joe Johnson and athletics director Doug Dickey had the Vols winning big in most of their varsity sports.
"I was blessed to have been there at a time when there was so much stability," Fulmer recalled. "Joe Johnson was an unbelievable leader and Doug Dickey was an unbelievable leader.
"We could get in a room and hash things out. I knew where my place was but we went all the way through to the guy that took care of the practice fields (in settling issues). We were a team, and that's what we've got to get back to."
Many fans believe Fulmer, who compiled a 152-52 record, can make Tennessee's athletics department a team again. He says he hasn't heard from his alma mater regarding the AD vacancy, however, either as a candidate or a consultant.
"Not really anything officially," he said. "Obviously, I'm in this community and I know a lot of folks but nothing officially (has been suggested), and I'm not expecting there to be. I think they're going to select a committee and go through the process."
Fulmer believes Tennessee's foundation is solid with some quality people filling critical roles.
"I think we've got a good president and we've got a good chancellor," he said. "I think they want to be here for a long period of time. Those are important pieces of this puzzle. Now we've got to get the same thing in whoever the athletic director is."
Once that piece is in place, Fulmer believes Tennessee can return to national prominence in its major sports.
"It all goes together, and it starts at the top," he said. "We've got the chancellor, we've got the president, and the trustees are all very mindful of what needs to be done. Now it's just getting this middle piece."