Executives from BBC Magazines and its adviser KPMG will present to the interested parties within two to three weeks. The BBC's commercial arm is working to have a deal in place by March.
The package of magazines, which includes titles such as Radio Times and the children's portfolio, is thought to be valued at no more than £200m.
BBC Worldwide declined to confirm the names of the interested parties, thought to include TV Choice-owner H Bauer and privately-owned German company Hubert Burda, which publishes Love It! magazine in the UK.
The possibility of a management buyout is also being speculated.
Top Gear, Gardener's World and Good Food will not be sold off but would instead be offered under licensing agreements with publishers.
The source said BBC Magazines is expected to set up a specialist unit that would meet with the magazines' new publishers on a weekly or monthly basis to ensure content complies with BBC guidelines.
The BBC is also thinking of holding on to the digital rights to the three magazine brands, the source said.
The BBC said it did not comment on speculation.
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