The presenter will leave the show when the present series ends in March.
Writing in the Daily Mail, John said: "When the present series comes to an end in March there will be someone else in the chair. I wish my successor well — but I'm not sure I envy them, whoever 'they' may be. What are the odds on the first female?"
He continued: "Mastermind is one of those programmes you tinker with at your peril. Allow a contender to choose a light-hearted subject and the cry goes out: 'Dumbing down!' Change the format even slightly and you are 'sexing up'."