The device, which would be fitted with a DAB chip, would plug into iPods and allow users to listen to live digital radio on the move.
Simon Nelson, controller of radio and music interactive at the BBC, said the discussions with Apple were in early stages but formed part of the BBC's plans to make digital radio as 'ubiquitous as analogue'.
He said: 'We are aware that the iPod makes up a significant proportion of the MP3 market and it doesn't have a DAB chip. It's very early stages, but we would like to enable everyone in the UK to listen digitally. We need to ensure there are devices available to enable people to listen to radio - especially on something that they already carry around.'
Nelson said the BBC was also talking with a number of other parties about the possibility of creating DAB plug-ins for a range of devices, including other MP3 players, mobile phones and in-car entertainment systems.
He added that the BBC was pressing for these devices because it has a responsibility to 'drive innovation in the market and stimulate ideas'. The devices would not restrict users to BBC radio stations.
The BBC will have to convince manufacturers there is a market for DAB-enabled plug-ins as their products are designed for multinational markets and take into account other European countries, where radio is not as popular as it is in the UK.
Nelson said: 'The problem in Europe is that radio is regarded as old-fashioned. Part of our job is to go to these manufacturers and explain that the situation in the UK is very different. We want to encourage manufacturers to use the UK as a beachhead.'
One possibility is to produce small batches of the plug-in devices, which would be tailored to the UK market. Nelson would not comment on the stage the discussions had reached, but said he hoped to see something on the market very soon.
He said: 'No one we've spoken to has told us that this is a barmy idea or that it is not going to work.'