The Match of the Day presenter is set to step down from his role at the end of the season.
Lineker confirmed last month his final show will be on the last day of the campaign.
However, he will continue to present the BBC's FA Cup coverage next season as well as action from the 2026 World Cup.
The 64-year-old will then depart the broadcaster once the tournament ends.
Ahead of his exit, Lineker discussed his future on television with Micah Richards and Alan Shearer on The Rest Is Football podcast.
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During the latest episode, he revealed he was offered the chance to appear on the next series of Celebrity Big Brother.
Lineker explained: "Do you know last week I got requests to go on Celebrity Big Brother."
The revelation prompted laughter from both Richards and Shearer before their co-host explained he turned down the approach.
He added: "My agent sent it through, and then jokingly he replied, 'Oh, yes. Gary's fee will be £50million'."
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Lineker continued: "He did it completely as a joke, obviously. And they came back and said, 'Oh, that's a little bit...that's not within our budget'."
Richards and Shearer both joked that the former England striker will keep getting such requests ahead of his BBC exit.
However, Lineker has no plans to appear on reality TV, as he said: "I can tell you now, don't bother asking."
Celebrity Big Brother returned to screens earlier this year on ITV with a new series scheduled for 2025.
Several former footballers have previously appeared on the show, including Vinnie Jones and Neil Ruddock as well as talkSPORT's Sports Bar host Jamie O'Hara and regular guest Jermaine Pennant.