According to a report in The Sunday Telegraph, the family would probably take more than 10% of the company and run it on behalf of the consortium.
For the Daily Mail & General Trust the move will reduce concerns from media watchdog Ofcom about fears that the group would control too large a stake of the UK newspaper market. Its bid and that of Richard Desmond will both likely spark inquiries.
The £500m bid by the Berry family was launched by Nicholas Berry, younger son of Lord Hartwell, and his nephew Caspar Gilroy. The Berrys had owned the papers since 1928.
Berry is understood to have been working on the bid for some time and has been in contact with Telegraph executives seeking support.
Lord Hartwell sold the papers to Lord Black when his business ran into trouble in 1985. The Berry family bid had been seen as a long shot but by bidding with DMGT and Cinven chances will rise.
Berry faces competition from Express Newspapers and venture capital firms Candover and Collins Stewart.
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