Martin Bashir, the BBC reporter behind interviews with Diana, Princess of Wales and Louise Woodward, the au pair convicted of manslaughter last year, met the men on Thursday, days after Ms Woodward criticised the fine line between "celebrity and notoriety" in the battle for television ratings.
The interview is likely to be broadcast as part of a Panorama programme when the public inquiry into Stephen Lawrence's death finishes later this year.
However, a representative from the London News Network, which makes news programmes for Carlton and LWT, has also met the five men with a view to making a programme.
David Norris, 21, Neil Acourt, 22, his brother Jamie, 21, Luke Knight, 20 and Gary Dobson, 22, have so far refused to answer direct questions about the stabbing at a south London bus stop in April 1993. In June, under duress, they appeared before the public inquiry but gave only evasive answers when questioned.
If, as seems likely, they are able to choose which station they talk to and perhaps who would do the interview, questions would be raised about the impartiality of the programme and whether the men were able to set their own agenda.
A spokesman for Panorama declined to elaborate on the programme-makers' plans: "We have a programme to make and we will see who appears on it."
Simon Bucks, programme controller of LNN, said: "We were aware that the BBC might be doing a programme and we thought it would be worthwhile looking at the possibilities of talking to them ourselves. We had a discussion with them and we made it quite clear that there could be no terms at all. We would obviously be interested in asking questions that have been avoided in the past or that have not been put to them ... There will be no terms, no deals and no payments."
Max Clifford, the public relations expert, who is thought to be behind the men's decision to talk publicly, said he had received a letter, from a group calling itself Justice, threatening that he would be "totally disabled" unless he severed all links with the five men.
"I have called in the police as a precaution and they are treating the matter very seriously," Mr Clifford said. "I have only given free advice to the men and I do not represent them."