The game show host's memoir, 'The Answer Is...: Reflections on My Life,' is out now.
"I joke with the audience all the time and I say, 'Betty White,' because they want somebody younger, somebody funnier," he said of the 98-year-old actress. "Betty and I have been friends for a long, long time."
In 2018, Trebek gave two other names for his possible replacement, Los Angeles Kings play-by-play announcer Alex Faust and CNN legal analyst Laura Coates.
"I mentioned to my producer before that the fellow who does play-by-play for the Los Angeles Kings, they should consider him," he said on OBJECTified of Faust, before turning to Coates.
"There is an attorney, Laura Coates, she's African American and she appears on some of the cable news shows from time to time," he said.
During his GMA sit-down, though, Trebek didn't sound like he had retiring on the mind as he discussed returning to work amid the coronavirus pandemic.
"We’ve redesigned our set to separate the contestants and myself a little bit more from them," he explained. "So we are taking all kinds of precautions. Our testing procedure now is done online."
The show will continue its schedule of filming five shows a day, two days per week.
"We’ll do three and take a short break, and then do the last two. And we’ll see how that goes," Trebek said. "And if it’s too much for me, we can always cut back a little bit, maybe do four a day."
Trebek went on to praise Jeopardy! as "the best kind of reality television."
"People watch it, and if they come up with one or two correct responses in that half hour, they feel pretty good about themselves," he said. "And that’s great."
In addition to enjoying his work on the show, Trebek is also thankful for his many fans, who have expressed their support following his stage 4 pancreatic cancer diagnosis.
"They are the most important elements in my life outside of my family and friends. Because they have expressed their feelings about me in so many positive ways that I can't help but be touched by what they have to say and by what I mean to them," he said. "It's humbling. It's nice to be humbled."
Despite all his positive feelings surrounding Jeopardy! and his fans, in his new memoir, The Answer Is...: Reflections on My Life, Trebek revealed that he won't continue on as the host forever.
"I'm the first to admit I'm not as sharp as I once was," Trebek writes. "... There will come a time when I can no longer do my job as host -- do it as well as the job demands, as well as I demand."
"Whenever it gets to that point, I’ll walk away… And Jeopardy! will be just fine," he continues. "It doesn’t matter who’s the host. It’s a quality program… There are other hosts out there who can do equally as good a job as me. I think Jeopardy! can go on forever."