The British-born Callendar, 51, is a surprise possibility. He has been at HBO for 15 years and has been responsible for award-winning dramas such as The Gathering Storm and Angels in America.
Among other names who are believed to have been approached by headhunters are Tony Hall, the Royal Opera House chief executive, Rupert Gavin, the chief executive of BBC Worldwide, and Jenny Abramsky, the head of BBC Radio.
BBC governors will appoint a director-general after ministers approve a new chairman to replace Gavyn Davies.
There has been speculation that Lord (Terry) Burns, a former Treasury mandarin and the chairman of Abbey, is a frontrunner for the £81,000-a-year role. He is an advisor to the culture secretary, Tessa Jowell, and is involved in the BBC Charter review process.
Burns is a close friend of both the prime minister, Tony Blair, and the former BBC director-general, Lord Birt, who is now a Downing Street advisor. However, his appointment could leave the Government open to charges of cronyism.
Among other names in the frame are Michael Grade, the chairman of Camelot; Patricia Hodgson, the former chief of the Independent Television Commission, and the broadcaster David Dimbleby.