Exponent, which owns thetrainline.com and the Ambassador Theatre Group, has emerged as a rival to publishing companies in the competition for assets such as the Radio Times.
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.
Bauer and H Bauer, , are understood to have neither withdrawn from the process nor had their offer rejected.
The sale process is believed to be complicated by terms in which titles linked to BBC programmes, such as Top Gear, will be offered under licensing deals and with oversight by a BBC editorial board.
It is understood that a management buyout also remains an option that financial advisor KPMG could be asked to explore.
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.
Exponent and BBC Magazines declined to comment.
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