Exponent, which owns thetrainline.com and the Ambassador Theatre Group, emerged last month as a rival to publishing companies in the competition for titles such as Radio Times and Top Gear, which were put up for sale by BBC Worldwide last year.
Sources with knowledge of the deal told Media Week that a period of exclusivity with Exponent was expected and that it was hoped a decision could be reached within two months.
However, they cautioned that the nature of the sell-off meant another party could emerge as a front runner.
"You never know in these auctions if someone else will come in at the last moment," said one source.
Bauer and H Bauer were believed to have put forward a joint offer to the BBC, but are now understood not to be in active talks over a sale.
Publishers Hubert Burda and Future, which both expressed an interest in the portfolio at the start of the process, are not involved at this stage, while it is understood that a management buyout also remains an option.
It emerged earlier this year that the BBC wanted to retain control over some leading titles, such as Top Gear. These are understood to be offered under licensing deals or contract publishing arrangements, with oversight by a BBC editorial board.
In its last financial year ending 31 March 2010, BBC Magazines reported revenue of £168.3m, and profits of £18.4m.
Out of that profit, lifestyle and specialist magazines including Radio Times, Good Food, Gardener's World and Top Gear, contributed £16.5m.
In March, Exponent acquired meat-free brand Quorn for £205m from Premier Foods, and Intermediate Capital Group.
BBC Worldwide was unavailable for comment.
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