According to audio obtained by the Houston Chronicle, Fisher was asked what it would take to beat Alabama other than the retirement of the 69-year-old Saban.
"We're going to beat his ass when he's there, don't worry," Fisher responded as the crowd laughed.
Fisher went on to say how much he respects Saban, whom he worked under at LSU from 2000 to '04.
Saban won his first national championships at LSU in 2004. He has gone on to win six more at Alabama, passing Paul "Bear" Bryant for the most all time.
Since Fisher arrived at Texas A&M in late 2017, the Aggies are 0-3 against Alabama and have been outscored 144-75, including a 52-24 loss last year.
Texas A&M finished last season 9-1 and No. 4 in the final College Football Playoff rankings.
"Eventually, that's going to be us," Fisher told the Touchdown Club. "I respect everything they do and how they do it, but we can do it just as good or be just as good or better, and we will."
Texas A&M players have already circled the Alabama game, if their comments in the spring are any indication.
"All I can say is, can't wait until the Bama game," defensive end DeMarvin Leal said last month.
Defensive tackle Jayden Peevy said he doesn't think the expectations are too much, too soon for the Aggies.
"We're not putting the pressure on ourselves. We just have a standard in this program now that we want to be the No. 1 team in the nation," he said. "We're going to practice like that, we're going to play like that. Every day we're coming out with the mindset to be the No. 1 team.
"I feel like this program is making steps toward being a big-time program, and we're going to see this season if we can beat Alabama."
Fisher told reporters last month it was great that his players have those expectations for themselves.
"It's great to have those goals," he said. "Now your daily habits have to match those goals when you can achieve them. And to me it's the whole thing. Are your daily habits, and what you do on a daily basis, matching up with your goals? If they don't match up, they're wasted goals. That's what we're learning to do. I'm glad to hear them talk about it, glad to hear them see it."
As far as when Saban might finally retire, the coach has given no indication he's ready to walk away.
"Coach Saban's here as long as Coach Saban can make a contribution to the team in a positive way, and that's my commitment to the organization, the university and the players," he said after Alabama's spring game last month. "If I felt like I couldn't do the job, for whatever reasons, then I think it would be time for somebody else to do it."