Although not fully public, the shortlist is believed to include a couple of surprise entries in BBC journalist and broadcaster David Dimbleby and former head of Channel 4 Michael Grade. Other shortlisted candidates include former Labour leader of the House of Lords Baroness Jay, and deputy BBC chairman Gavyn Davies.
There is believed to be a fifth name as well, which has yet to be revealed.
Sir Christopher Bland was appointed as BT chairman in April and took over from Sir Iain Vallance on May 1. Controversially, no plans were made to move him from his job of BBC chairman until a replacement could be found.
Grade surprised the industry when he applied for the job because he has been recently quoted as saying that there were two certainties in his life: "One is that I would like to be chairman of the BBC. The second is that no one will ever ask me."
If Dimbleby got the £82,000-a-year, three-day-a-week job he would have to give up the broadcasting and journalism career that he has built up over 40 years. Dimbleby is one of the BBC's most authoritative figures and currently presides over high-brow political talkshow Question Time.
However, Dimbleby could inch ahead of other favourites because he has managed to keep his political preferences close to his chest.
Other candidates with high-profile Labour links will likely be sidelined because of director general Greg Dyke's former allegiances with the Labour Party. Another Labour-friendly appointment at the helm of the public service broadcaster would raise questions about its political impartiality.
The wife of millionaire Goldman Sachs economist Davies works for chancellor of the exchequer Gordon Brown, while Baroness Jay, who has experience of broadcasting from working on Panorama during the Seventies, is hugely unpopular with the right-wing press.
The DCMS would not confirm any names on the list. However, a spokeswoman said that interviews, to be conducted by a panel of civil servants, would take place over the coming weeks.
Recommendations will then be made to media secretary Tessa Jowell and a decision will be reached with the approval of Tony Blair and Buckingham Palace.
No decision can be reached until the new leader of the Conservative Party is appointed, which is expected to happen around September 7. This is to ensure that both sides of the political spectrum are catered for.
This year, the chairmanship of the BBC was advertised in the national press for the first time, in an effort to attract a wide range of candidates.