Germany-based Bauer Media, the publisher of Closer and Heat magazines, is one among four bidders to acquire all or part of BBC Magazines.
The Sunday Times reported that Bauer Media is in the running to acquire the BBC's £100m magazine portfolio which includes Radio Times, Top Gear and Good Food.
Following a strategy review, the BBC announced in September that it would sell off its magazines division. It is the UK's fourth largest magazine publisher in terms of circulation.
The strategy review had called on the broadcaster to focus on its international operations and "move away from physical media".
A bidder could acquire all or part of BBC Magazines, involving a majority equity stake in the business of up to 85 per cent.
Only four parties, including Bauer Media, are now part of the auction, down from the initial 30 that expressed interest in BBC Magazines.
National Magazines, publisher of Cosmopolitan, Good Housekeeping and Men's Health, is no longer part of the auction.
Instead, it was now favourite to acquire the global titles of France's Lagardere, including Inside Soap and Psychologies in Britain, valued at £600m.