He declined to identify which stars he had in mind.
Certain celebrities have enjoyed huge success - with Alex Ferguson's tell-all book notching up nearly 700,000 sales so far this year.
Other hits have been Roy Keane's The Second Half, selling 149,000 copies, and Lynda Bellingham: There's Something I've Been Dying To Tell You, selling 265,000 copies.
But for every successful book there are many more flops and Mr Redmayne says he feels it's now time to pull back.
The publishing chief - who took charge of Rupert Murdoch's HarperCollins last year - was speaking as annual accounts revealed the company's revenues dropped nearly six per cent to £180 million in the year to June.
He claimed part of the reason for the fall in revenue was his 'strategic decision' to avoid 'unprofitable' non-fiction publishing - and he pointed out that operating profits actually jumped 80 per cent to £5 million.
He said: 'I felt the company had embraced some quite risky celebrity non-fiction. A lot of these books were hugely expensive and they were not necessarily going to back-list well.
Speaking to The Times, he added: 'We want a broad swathe of publishing, but historically, HarperCollins, and indeed a lot of other publishers, had been making some very, very big bets on big celebrity autobiographies.
'That celebrity non-fiction market, in my opinion, has peaked. It's still there, there's still a market for it, but it is coming down.
'I think the prices - the advance that we pay the authors - needs to reflect that.'
Last year Pippa Middleton was dropped by Penguin after her party planning book Celebrate sold only 2000 copies in the first week.
The Duchess of Cambridge's sister was said to have received a staggering £400,000 fee for the book in advance.
The Bookseller Magazine recently reported that sales of biographies and autobiographies had slumped four per cent in 2014.
Patrick Neale, the owner of Jaffe and Neale's bookshop in Oxfordshire, told the magazine: 'I have always asked when the bubble is going to burst on celebrity titles and to date I have been proved wrong, but actually this might be the year it has finally happened.
'Sales of Stephen Fry and Michael Palin books have been low, which is surprising.'
A novel by the online video blogger Zoe Sugg, known as Zoella, has been the biggest success of the Christmas period - despite critics commenting on her use of a ghost writer.
Her book Girl Online sold more than 78,000 copies in its first week - more than JK Rowling, Dan Brown or EL James achieved with their first books.
- The Daily Mail