Sorry, Survivor fans: There will not be an all-winners season. At least, not if longtime host and executive producer Jeff Probst has his way.

“We can’t do all winners,” Probst, 56, tells Us Weekly. “As a producer, I would never suggest it. I would say it’s not a good idea.”

Certainly, there is no shortage of contestants in terms of numbers. Probst talked to Us on a remote island in Fiji during production of the upcoming 38th season of the veteran reality show, set to premiere in 2019. (The current Survivor: David vs. Goliath is Edition No. 37.)

The problem, he says, is that not all the previous winners are compelling enough to return, and the memorable ones — such as “Boston” Rob Mariano, Parvati Shallow and John Cochran — don’t want to spend another 36 days trying to outwit, outplay and outlast contestants for another shot at $1 million.

“We have 10 great winners that you’d want to see play again,” he says. “We don’t have 20. We don’t have 18. Some of the winners don’t want to play again. Some of the greats are like, ‘No, we’re done.’”

Still, Probst admits that the show’s rabid fans — as well as higher-ups at his very own network — have inquired about it.

“CBS wants to do it,” he says. “They’re pitching me all the time. And I’m going, ‘I’ll sit down with you and show you the list!’ We don’t have it. And if I sat down and we wasted our time and I walked you through all our winners, you would say, ‘Oh, you’re right. You don’t have a season.’ We have a tribe of winners, that’s it.”

Indeed, Probst acknowledges that it’s possible that an upcoming edition could incorporate all winners on one of the tribes: “We could do winners versus another group. That’s an idea.”

Survivor: David vs. Goliath premieres on CBS Wednesday, September 26, at 8 p.m.